#Setting up

Property Value Prediction Model - predictive model of price incorporating structural and locational characteristics - summary statistics w variable descriptions - correlation matrix - 4 home price correlation scatterplots - 1 map of dep variable (sale price) - 3 maps of 3 most interesting independent variables (factors we choose) - testing and training dataset??? - discussion of performance - plot of predicted prices as function of observed prices - map of residuals

Introduction

The Seattle housing market is a vibrant and complex sector that encapsulates the city’s economic growth and diverse population. Seattle offers a mix of modern high-rise apartments, classic craftsman houses, and waterfront properties, which serve the varied preferences of its residents. The housing prices in Seattle are shaped by an array of factors, including location, architectural style, age of the property, and proximity to amenities like parks, schools, and public transport.

This project evaluates factors affecting housing prices to create an accurate and generalizable OLS regression model to predict them. Housing prices in Seattle have been subject to fluctuations over the years, influenced by various factors such as the neighborhood, property type, and home condition. Sale prediction algorithms are crucial tools that help different stakeholders in the housing market make informed decisions, identify inequalities, and ensure the real estate market’s overall health and fairness.

Building a predictive model for property valuation is challenging, requiring selecting the right features, addressing collinearity among variables, choosing appropriate modeling techniques, and ensuring interpretability. Creating this model was an iterative process that involved multiple rounds of trial and error, particularly in attempts to minimize the errors in predictions. The maps, correlation matrix, and scatterplots illustrate various variables that were considered, wrangled, and filtered as part of the data analysis process.

if (!require(pacman)){install.packages("pacman"); library(pacman)}
p_load (sf, tidyverse, knitr, kableExtra, rmarkdown, tidycensus, dplyr, scales, stringr, ggcorrplot, readxl, data.table, caTools, tmap, stargazer, spdep, caret, ckanr, FNN, grid, gridExtra, jtools, broom, tufte, rmarkdown, brewer.pal, ggplot2)
census_api_key("b3eda1fa84dde3c5ad443fd407d48f2584ab2726", overwrite = TRUE)

Data Wrangling

Census, OpenData Seattle and provided Dataset

Provided Dataset and Internal Variables

The code below is used to import the foundational dataset for our model. This dataset contains information on home sales prices and property characteristics in Seattle, Kings County for the years 2014 and 2015. The model we are developing is designed to make predictions about home prices and utilizes specific property attributes from this dataset to enhance the accuracy of those predictions.

kingsCounty <- read.csv("kc_house_data.csv")
kingsCoSF <- st_as_sf(kingsCounty, coords = c("long", "lat"), crs = 4326)

seattleTreeCanopy <- read.csv("Seattle_Tree_Canopy_2016_2021_RSE_Census_Tracts.csv")

crs <- st_crs(kingsCoSF)
print(crs)

Getting census tracts data from HUD USPS Crosswalk files to assign census tracts to the original data.

#Data from HUD USPS Zipcode Crosswalk files
hud_data <- read_excel("ZIP_TRACT_032015.xlsx")

desired_zips <- c("98101", "98102", "98103", "98104", "98105", "98106", "98107", "98108", 
                  "98109", "98111", "98112", "98113", "98114", "98115", "98116", "98117", 
                  "98118", "98119", "98120", "98121", "98122", "98123", "98124", "98125", 
                  "98126", "98131", "98132", "98133", "98134", "98135", "98136", "98138", 
                  "98144", "98145", "98146", "98148", "98154", "98155", "98158", "98160", 
                  "98161", "98164", "98166", "98168", "98171", "98174", "98177", "98178", 
                  "98188", "98198", "98199")
#filtering out data that's not Seattle

seattleData <- kingsCoSF %>%
  filter(zipcode %in% c("98101","98102","98103","98104","98105", "98106","98107", "98108","98109","98111","98112","98113",'98114","98115"."98116","98117","98118","98119","98120","98121","98122","98123","98124","98125","98126","98131","98132',"98133","98134","98135","98136","98138","98144","98145","98146","98148","98154","98155","98158","98160","98161","98164","98166","98168","98171","98174","98177","98178","98188","98198","98199"))

seattleData$zipcode <- as.character(seattleData$zipcode)
hud_data$ZIP <- as.character(hud_data$ZIP)

#Filtering HUD data for zipcodes of interest
hud_data_filtered <- hud_data[hud_data$ZIP %in% desired_zips, ]

#Merging the filtered HUD dataset with the seattle housing data
seattleData <- merge(seattleData, hud_data_filtered, by.x = "zipcode", by.y = "ZIP", all.x = TRUE)

#removing extra columns
seattleData <- seattleData %>%
  select(-OTH_RATIO, -RES_RATIO, -TOT_RATIO, -BUS_RATIO)

seattleData <- seattleData %>%
  mutate(TRACT = str_sub(TRACT, -6)) # Keep the last 6 characters


seattleData <- seattleData %>%
  filter(yr_built > 0) 

#categorizing based on basement presence
seattleData <- seattleData %>%
  mutate(basementPresent = case_when(
    sqft_basement == 0 ~ 'No Basement',
    sqft_basement >= 1 ~ 'Basement'))

#categorizing based on condition
seattleData <- seattleData %>%
  mutate(conditionType  = case_when(
    condition == '1' ~ 'Very Poor',
    condition == '2' ~ 'Poor',
    condition == '3' ~ 'Average',
    condition == '4' ~ 'Good',
    condition == '5' ~ 'Very Good'))

seattleData <- seattleData %>%
  mutate(houseSize = case_when(
    sqft_living >= 2000 ~ 'Big',
    sqft_living <= 1999 ~ 'Small'))

seattleDisability <- seattleTreeCanopy %>%
  select(PCT_ADULT_WITH_DISABILITIES)


#summary statistics should ideally combine the different datasets 
summary(seattleData)
##    zipcode                id                date               price        
##  Length:64080       Min.   :1.200e+06   Length:64080       Min.   :  78000  
##  Class :character   1st Qu.:2.011e+09   Class :character   1st Qu.: 306000  
##  Mode  :character   Median :3.973e+09   Mode  :character   Median : 414050  
##                     Mean   :4.484e+09                      Mean   : 502873  
##                     3rd Qu.:6.909e+09                      3rd Qu.: 587812  
##                     Max.   :9.900e+09                      Max.   :7700000  
##     bedrooms        bathrooms      sqft_living       sqft_lot     
##  Min.   : 0.000   Min.   :0.000   Min.   :  380   Min.   :   520  
##  1st Qu.: 3.000   1st Qu.:1.000   1st Qu.: 1240   1st Qu.:  4000  
##  Median : 3.000   Median :1.750   Median : 1600   Median :  6099  
##  Mean   : 3.191   Mean   :1.881   Mean   : 1777   Mean   :  6987  
##  3rd Qu.: 4.000   3rd Qu.:2.500   3rd Qu.: 2150   3rd Qu.:  8410  
##  Max.   :33.000   Max.   :8.000   Max.   :12050   Max.   :137214  
##      floors        waterfront            view          condition    
##  Min.   :1.000   Min.   :0.000000   Min.   :0.0000   Min.   :1.000  
##  1st Qu.:1.000   1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:3.000  
##  Median :1.000   Median :0.000000   Median :0.0000   Median :3.000  
##  Mean   :1.469   Mean   :0.008146   Mean   :0.2534   Mean   :3.445  
##  3rd Qu.:2.000   3rd Qu.:0.000000   3rd Qu.:0.0000   3rd Qu.:4.000  
##  Max.   :3.500   Max.   :1.000000   Max.   :4.0000   Max.   :5.000  
##      grade          sqft_above   sqft_basement       yr_built   
##  Min.   : 4.000   Min.   : 380   Min.   :   0.0   Min.   :1900  
##  1st Qu.: 7.000   1st Qu.:1060   1st Qu.:   0.0   1st Qu.:1933  
##  Median : 7.000   Median :1320   Median :   0.0   Median :1953  
##  Mean   : 7.295   Mean   :1453   Mean   : 323.3   Mean   :1957  
##  3rd Qu.: 8.000   3rd Qu.:1660   3rd Qu.: 630.0   3rd Qu.:1979  
##  Max.   :13.000   Max.   :8570   Max.   :3480.0   Max.   :2015  
##   yr_renovated    sqft_living15    sqft_lot15        TRACT          
##  Min.   :   0.0   Min.   : 690   Min.   :   651   Length:64080      
##  1st Qu.:   0.0   1st Qu.:1330   1st Qu.:  4000   Class :character  
##  Median :   0.0   Median :1560   Median :  6050   Mode  :character  
##  Mean   : 108.2   Mean   :1676   Mean   :  6611                     
##  3rd Qu.:   0.0   3rd Qu.:1910   3rd Qu.:  8292                     
##  Max.   :2015.0   Max.   :4950   Max.   :128066                     
##           geometry     basementPresent    conditionType       houseSize        
##  POINT        :64080   Length:64080       Length:64080       Length:64080      
##  epsg:4326    :    0   Class :character   Class :character   Class :character  
##  +proj=long...:    0   Mode  :character   Mode  :character   Mode  :character  
##                                                                                
##                                                                                
## 
seattleData <- seattleData %>%
  mutate(bedroomIndex = case_when(
    bedrooms >= 1 ~ 1, 
    bedrooms < 1 ~ 0))

seattleData$bedroomIndex[is.na(seattleData$bedroomIndex)] <- 0

lm(bedrooms ~ sqft_living, data = seattleData)
## 
## Call:
## lm(formula = bedrooms ~ sqft_living, data = seattleData)
## 
## Coefficients:
## (Intercept)  sqft_living  
##   1.8342456    0.0007639
for(i in 1:nrow(seattleData))
{
  if(seattleData$bedroomIndex[i] == 0)
  {seattleData$bedrooms[i] = 1.9054627 +  0.0007142*seattleData$sqft_living}
}

seattleData$bedrooms <- round(seattleData$bedrooms, digits = 0)
seattleData <- seattleData %>%
  mutate(pricePerFt2 = (price/sqft_living)) #might need to do the linear regression bathroom and rooms for this stuff

seattleData <- seattleData %>%
  mutate(buildingAge = (2015 -(yr_built)))

Census Data Collection

The census information from 2021 offers a detailed look at the community and housing in King County, including stuff like how many people live there, what types of homes they have, and income levels. To use this data with housing prices from 2015, we need to remember that things might have changed over those six years, which could affect the home prices in Seattle.

acsVariables2015 <- load_variables(2015, "acs5", cache = TRUE)

# 2021, A

# Retrieve ACS data for Seattle tracts in 2015
kcTracts <- get_acs(
  geography = "tract",
  variables = c(
    "B01003_001",   # Total Population
    "B19013_001",   # Median Household Income
    "B25058_001",   # Median Rent
    "B25008_002",   # Owner-Occupied Units
    "B25008_003",   # Renter-Occupied Units
    "B07001_032",   # Same House 75 Years Ago
    "B07001_017",   # Same House 1 Year Ago
    "B25088_003",   # Median Selected Monthly Owner Costs (homes without a mortgage)
    "B25088_002",   # Median Selected Monthly Owner Costs (homes with a mortgage)
    "B15003_022",   # Educational Attainment: Bachelor's Degree
    "B17001_002",   # Percentage of Population Below the Poverty Level
    "B28002_004",   # Percentage of Housing Units with High-Speed Internet
    "B25044_003",   # Percentage of Housing Units with No Vehicle Available
    "B02001_002",   # Race and Ethnicity: White Alone
    "B02001_003",   # Race and Ethnicity: Black or African American Alone
    "B03001_003"    # Hispanic or Latino Origin of Population
  ),
  year = 2021,
  state = "WA",#washington
  county = "King",#kings county
  geometry = TRUE,
  output = "wide"
)%>%
  select(-NAME, -ends_with("M")) %>%
  rename(totalPop = B01003_001E,                           # Total Population
         medIncome = B19013_001E,                         # Median Household Income
         medRent = B25058_001E,                           # Median Rent
         ownerUnits = B25008_002E,                        # Owner-Occupied Units
         renterUnits = B25008_003E,                       # Renter-Occupied Units
         sameHouse75 = B07001_032E,                      # Same House 75 Years Ago
         sameHouse1 = B07001_017E,                       # Same House 1 Year Ago
         medianNoMortgage = B25088_003E,          # Median Selected Monthly Owner Costs (homes without a mortgage)
         medianMortgage = B25088_002E,        # Median Selected Monthly Owner Costs (homes with a mortgage)
         bachelors = B15003_022E,                      # Educational Attainment: Bachelor's Degree
         belowPoverty = B17001_002E,                  # Percentage of Population Below the Poverty Level
         highSpeedInternet = B28002_004E,  # Percentage of Housing Units with High-Speed Internet
         noVehicle = B25044_003E,           # Percentage of Housing Units with No Vehicle Available
         White = B02001_002E,                         # Race and Ethnicity: White Alone
         Black = B02001_003E,                         # Race and Ethnicity: Black or African American Alone
         hispanicLatino = B03001_003E                     # Race and Ethnicity: Hispanic or Latino
         )
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |==                                                                    |   2%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |======                                                                |   8%  |                                                                              |=======                                                               |   9%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |==========                                                            |  14%  |                                                                              |===========                                                           |  15%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  25%  |                                                                              |======================                                                |  32%  |                                                                              |========================                                              |  34%  |                                                                              |=========================                                             |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=================================                                     |  47%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  64%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |======================================================================| 100%
# Transform the data to ESRI:102728 projection
kcTracts <- kcTracts %>% st_transform(st_crs(seattleData)) #need to add projection to kc stuff earlier

#also need to filter out the tracts for seattle!!!! 
seattleSchools <- read.csv("Seattle_Public_Schools_Sites_2023-2024.csv")
seattleSchools <- st_as_sf(seattleSchools, coords = c("Longitude", "Latitude"), crs = 4326) %>%
  st_transform(st_crs(seattleData))

#mapping nearest school
closestSchool <- sf::st_nearest_feature(seattleData, seattleSchools)

#converting into rsgeo geometries
x <- rsgeo::as_rsgeo(seattleData)
y <- rsgeo::as_rsgeo(seattleSchools)

## Calculating distance
seattleData$dist2NearestSchool <- rsgeo::distance_euclidean_pairwise(x, y[closestSchool])

#Police Stations
kcPS <- read.csv("Police_Station_Locations_in_King_County___kcp_loc_point.csv")

seattlePS <- kcPS %>%
  filter(ZIPCODE %in% c("98101","98102","98103","98104","98105", "98106","98107", "98108","98109","98111","98112","98113",'98114","98115"."98116","98117","98118","98119","98120","98121","98122","98123","98124","98125","98126","98131","98132',"98133","98134","98135","98136","98138","98144","98145","98146","98148","98154","98155","98158","98160","98161","98164","98166","98168","98171","98174","98177","98178","98188","98198","98199"))

kcPS <- st_as_sf(seattlePS, coords = c("X", "Y"), crs = 4326) %>%
  st_transform(st_crs(seattleData))



# Checking CRS of seattleData and seattlePS
crs_seattleData <- st_crs(seattleData)
crs_seattlePS <- st_crs(seattlePS)

print(crs_seattleData)
## Coordinate Reference System:
##   User input: EPSG:4326 
##   wkt:
## GEOGCRS["WGS 84",
##     ENSEMBLE["World Geodetic System 1984 ensemble",
##         MEMBER["World Geodetic System 1984 (Transit)"],
##         MEMBER["World Geodetic System 1984 (G730)"],
##         MEMBER["World Geodetic System 1984 (G873)"],
##         MEMBER["World Geodetic System 1984 (G1150)"],
##         MEMBER["World Geodetic System 1984 (G1674)"],
##         MEMBER["World Geodetic System 1984 (G1762)"],
##         MEMBER["World Geodetic System 1984 (G2139)"],
##         ELLIPSOID["WGS 84",6378137,298.257223563,
##             LENGTHUNIT["metre",1]],
##         ENSEMBLEACCURACY[2.0]],
##     PRIMEM["Greenwich",0,
##         ANGLEUNIT["degree",0.0174532925199433]],
##     CS[ellipsoidal,2],
##         AXIS["geodetic latitude (Lat)",north,
##             ORDER[1],
##             ANGLEUNIT["degree",0.0174532925199433]],
##         AXIS["geodetic longitude (Lon)",east,
##             ORDER[2],
##             ANGLEUNIT["degree",0.0174532925199433]],
##     USAGE[
##         SCOPE["Horizontal component of 3D system."],
##         AREA["World."],
##         BBOX[-90,-180,90,180]],
##     ID["EPSG",4326]]
print(crs_seattlePS)
## Coordinate Reference System: NA
# Checking class of the datasets and ensuring crs is same
print(class(seattleData))
## [1] "sf"         "data.frame"
print(class(seattlePS))
## [1] "data.frame"
if (!inherits(seattlePS, "sf")) {
  seattlePS <- st_as_sf(seattlePS, coords = c("X", "Y"), crs = 4326)
}

# Transforming seattlePS to match the crs of seattleData
if (!st_crs(seattleData) == st_crs(seattlePS)) {
  seattlePS <- st_transform(seattlePS, st_crs(seattleData))
}

#mapping nearest police stations
closestPS <- sf::st_nearest_feature(seattleData, seattlePS)

#converting into rsgeo geometries
x <- rsgeo::as_rsgeo(seattleData)
y <- rsgeo::as_rsgeo(seattlePS)

#calculating distance
seattleData$dist2NearestPS <- rsgeo::distance_euclidean_pairwise(x,y[closestPS])

#Transit Stops
kcTransitStops <- read.csv("Transit_Stops_for_King_County_Metro___transitstop_point.csv")

seattleTransitStops <- kcTransitStops %>%
  filter(ZIPCODE %in% c("98101","98102","98103","98104","98105", "98106","98107", "98108","98109","98111","98112","98113",'98114","98115"."98116","98117","98118","98119","98120","98121","98122","98123","98124","98125","98126","98131","98132',"98133","98134","98135","98136","98138","98144","98145","98146","98148","98154","98155","98158","98160","98161","98164","98166","98168","98171","98174","98177","98178","98188","98198","98199"))

kcTransitStops <- st_as_sf(seattleTransitStops, coords = c("X", "Y"), crs = 4326) %>%
  st_transform(st_crs(seattleData))

kcTransitStops <- st_transform(kcTransitStops, st_crs(seattleData))

closestTransitStop <- st_nearest_feature(seattleData, kcTransitStops)

seattleData$dist2NearestTransitStop <- st_distance(seattleData, kcTransitStops[closestTransitStop,], by_element = TRUE)

# converting it to character
seattleData$dist2NearestTransitStop <- as.character(seattleData$dist2NearestTransitStop)

# removing '[m]' from the string
seattleData$dist2NearestTransitStop <- sub("\\s\\[m\\]", "", seattleData$dist2NearestTransitStop)

# converting the results back to numeric
seattleData$dist2NearestTransitStop <- as.numeric(seattleData$dist2NearestTransitStop)
kcTracts <- kcTracts %>%
  mutate(PctWhite = ((White/totalPop)*100),
         PctBlack = ((Black/totalPop)*100),
         PctHispanic = ((hispanicLatino/totalPop)*100),
         PctBachelors = ((bachelors/totalPop)*100),
         PctPoverty = ((belowPoverty/totalPop)*100))

# Filter kctracts to include only the specified GEOID range
kcTracts_filtered <- kcTracts %>%
  filter(as.numeric(GEOID) >= 53033000100 & as.numeric(GEOID) <= 53033030100)

#removing extra columns
kcTracts_filtered <- kcTracts_filtered %>%
  select(-medRent, -ownerUnits, -renterUnits, -sameHouse75, -sameHouse1, -medianNoMortgage, -medianMortgage, -bachelors, -belowPoverty, -highSpeedInternet, -noVehicle, -Black, -White, -hispanicLatino, -totalPop, -geometry)

# Check the result
head(kcTracts_filtered)
kcTracts_filtered <- kcTracts_filtered %>%
  rename(TRACT = GEOID) %>% # Rename GEOID to TRACT
  mutate(TRACT = str_sub(TRACT, -6)) # Keep the last 6 characters


# Joining data from two datasets
seattleData <- st_join(seattleData, kcTracts_filtered)

Summary Statistics

Summary statistics provide a quick snapshot of key attributes of your dataset, such as the average values, variability, and distribution across different variables, which can indicate trends and outliers in your data. They’re essential for understanding the general behavior of the dataset before diving into deeper analysis.

Summary Statistics: Internal Variables

These statistics provide an overview of the central tendency, spread, and range of the internal variables for Seattle homes, which include prices, price per square foot, living area size, year built, number of rooms etc.

InternalVariables <- seattleData

InternalVariables <- st_drop_geometry(InternalVariables)

InternalVariables <- InternalVariables %>%
  dplyr::select("price", "pricePerFt2", "sqft_living", "yr_built", "bedrooms", "bathrooms", "condition", "sqft_basement", "sqft_lot")

stargazer(as.data.frame(InternalVariables), type="text", digits=1, title = "Descriptive Statistics for Seattle Homes Internal Variables", out = "Training_seattleInternal.txt")
## 
## Descriptive Statistics for Seattle Homes Internal Variables
## =========================================================
## Statistic       N      Mean    St. Dev.   Min      Max   
## ---------------------------------------------------------
## price         64,080 502,872.6 347,834.7 78,000 7,700,000
## pricePerFt2   64,080   286.9     116.4    87.6    798.1  
## sqft_living   64,080  1,776.6    792.4    380    12,050  
## yr_built      64,080  1,957.0    31.8    1,900    2,015  
## bedrooms      64,080    3.2       1.1      1       33    
## bathrooms     64,080    1.9       0.8     0.0      8.0   
## condition     64,080    3.4       0.7      1        5    
## sqft_basement 64,080   323.3     423.3     0      3,480  
## sqft_lot      64,080  6,986.9   6,015.4   520    137,214 
## ---------------------------------------------------------

It is observed that the average sale price of homes in Seattle is approximately 502,782.6 USD. The sale prices vary quite widely with a high standard deviation, indicating a more heterogenous market.

The average age for a house in Seattle is approximately 65 years indicating a large share of the market is held by homes constructed a long time ago.

Summary Statistics: Demographic Variables

These statistics provide an overview of the central tendency, spread, and range of the internal variables for Seattle homes, which include median income, percentage of white population, percentage of black population, percentage of hispanic population, percentage of population with a bachelor’s degree and percentage of population living in poverty.

DemographicVariables <- seattleData

DemographicVariables <- st_drop_geometry(DemographicVariables)

DemographicVariables <- DemographicVariables %>%
  dplyr::select("PctWhite", "PctBlack", "PctHispanic", "PctBachelors", "PctPoverty", "medIncome") 

stargazer(as.data.frame(DemographicVariables), type="text", digits=1, title = "Descriptive Statistics for Seattle Homes Demographic Variables", out = "Training_seattleSpatial.txt")
## 
## Descriptive Statistics for Seattle Homes Demographic Variables
## =====================================================
## Statistic      N      Mean    St. Dev.  Min     Max  
## -----------------------------------------------------
## PctWhite     63,970   63.6      18.0    7.3    93.1  
## PctBlack     63,970    7.4      7.6     0.0    43.3  
## PctHispanic  63,970   10.1      7.4     0.8    39.1  
## PctBachelors 63,970   24.9      8.4     2.8    53.4  
## PctPoverty   63,970    8.4      5.3     0.0    46.0  
## medIncome    63,760 108,185.7 34,358.2 35,684 250,001
## -----------------------------------------------------

The table presents descriptive statistics for demographic variables related to Seattle homes, offering insights into the characteristics of the population in different areas.

On average, approximately 63.6% of the population in the observed areas is White. The range of White population percentages spans from 7.3% to 93.1%, indicating a wide diversity in racial composition across different areas of Seattle. The same does not hold true for Black and Hispanic population percentages indicating the presence of White-majority neighborhoods in different parts of Seattle.

The average median household income in the observed areas is $108,185.2 with approximately 8.4% of the population in the observed areas falls below the poverty level, on average.

Summary Statistics: Spatial Variables

These statistics provide an overview of the central tendency, spread, and range of the internal variables for Seattle homes, which include distances to key nearest amenities.

SpatialVariables <- seattleData 

SpatialVariables <- st_drop_geometry(SpatialVariables)

SpatialVariables <- SpatialVariables %>%
  dplyr::select("dist2NearestSchool", "dist2NearestPS", "dist2NearestTransitStop") 

stargazer(as.data.frame(SpatialVariables), type="text", digits=1, title = "Descriptive Statistics for Seattle Homes Spatial Variables (Figure 4.1)", out = "Training_seattleSpatial.txt")
## 
## Descriptive Statistics for Seattle Homes Spatial Variables (Figure 4.1)
## ===========================================================
## Statistic                 N    Mean  St. Dev.  Min    Max  
## -----------------------------------------------------------
## dist2NearestSchool      64,080 0.02    0.03   0.000   0.2  
## dist2NearestPS          64,080 0.02    0.01   0.001   0.1  
## dist2NearestTransitStop 64,080 191.0  183.4    2.8  2,330.9
## -----------------------------------------------------------

These statistics offer insights into the spatial characteristics of Seattle neighborhoods where the “Mean” in each case represents the average distance to a specific amenity like police stations, schools and transit stops from a listed property.

Scatterplots

The following code generates a set of scatterplots to explore the relationships between the sale price of homes and various continuous variables. The data is first filtered to exclude observations where the sale_price is less than 5,000,000 to remove any outliers. For the remaining data, a set of scatterplots is created. The scatterplots help visualize the relationships between the sale price of homes and each of the continuous variables, as well as the direction and strength of these relationships. The regression lines indicate whether there is a linear trend in the data.

The scatterplots illustrate that in Seattle, home prices have a positive relationship with square footage and percentage of residents with a bachelor’s degree, suggesting larger homes and more educated neighborhoods tend to have higher property values. Conversely, there’s no clear pattern with the age of the house, indicating that newer does not necessarily mean more expensive in this market.

Correlation Matrix

The correlation matrix provides a numerical summary of how different variables in the housing dataset are related to one another. The correlation matrix indicates that home prices in the Seattle housing dataset are positively correlated with the size of the living area and the number of bathrooms, meaning larger homes and those with more bathrooms tend to be more expensive. There seems to be a slight negative correlation between the price of homes and the distance to the nearest public school and transit stop, implying that homes closer to schools may command higher prices. The zeros in the correlation matrix highlight that there is no linear relationship between the home price and the year built or between the distances to nearest public school and transit stops, which stands out, suggesting that newer homes are not necessarily priced higher and that proximity to these amenities does not uniformly affect home values.

int_variables <- c("price", "condition", "sqft_living", "yr_built", "bedrooms", "bathrooms", "dist2NearestSchool", "dist2NearestPS", "dist2NearestTransitStop", "PctWhite", "PctBachelors", "medIncome")

seattleDatacorr <- seattleData %>% 
  st_drop_geometry() %>% 
  select(all_of(int_variables)) %>% 
  na.omit()

corr <- cor(seattleDatacorr)
rounded_corr <- round(corr, 1)
ggcorrplot(rounded_corr,
           type = "lower",
           lab = TRUE,
           lab_size = 2,
           colors = c("#d7191c", "#ffffbf", "#2c7bb6"),
           title = "Correlation Matrix of Housing Dataset",
           ggtheme = theme_bw())

Exploratory Mapping and analysis

#making a function for the quintile breaks
qBr <- function(data, var_name) {
  # Extract the variable from the dataframe
  var <- data[[var_name]]
  # Calculate quintiles
  quintiles <- quantile(var, probs = seq(0, 1, by = 0.25), na.rm = TRUE)
  # Return breaks
  return(quintiles)
}

#function for map theme

mapTheme <- function() {
  tm_shape() +
    tm_layout(
      # Customize map background and frame
      background.color = "lightblue",
      frame = FALSE,
      
      # Customize text style and color
      title.text.size = 1.2,
      text.color = "darkblue",
      
      # Customize legend appearance
      legend.position = c("right", "bottom"),
      legend.bg.color = "lightgray",
      legend.text.size = 0.8,
      legend.title.size = 0.9,
      
      # Add more customizations as needed
    )
}

Mapping sale price

# Creating quintiles from the price variable
seattleData$priceQuintiles <- cut(seattleData$price, 
                                  breaks = quantile(seattleData$price, probs = seq(0, 1, by = 0.2)), 
                                  include.lowest = TRUE, 
                                  labels = FALSE)

# Converting the quintiles into a factor
seattleData$priceQuintiles <- factor(seattleData$priceQuintiles)

#palette
palette <- c('#d7191c', '#fdae61', '#ffffbf', '#abd9e9', '#2c7bb6')

#mapping sale price
ggplot() +
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +
  geom_sf(data = seattleData, aes(colour = priceQuintiles)) +  # Ensure q5(price) is a factor
  scale_color_manual(values = palette,  # Use scale_color_manual to match the color aesthetic
                     labels = qBr(seattleData, "price"),
                     name = "Quintile Breaks:\nSale Price") +  # Correct label text
  labs(title = "Properties by Sale Price", subtitle = "Seattle 2015") +
  theme_void()

The map shows the distribution of property sale prices across Seattle in 2015, with areas color-coded by quintile to indicate the range of sale prices. Red indicates the lowest price quintile while blue represents the highest, illustrating the spatial patterns of housing affordability or value within the city. This could reflect various socioeconomic factors, urban development patterns, and housing demand in different neighborhoods.

Mapping internal variables

The maps visualize the spatial distribution of basements, property conditions and property size across Seattle’s residential properties in 2015.

#palette
palette <- c('#d7191c', '#fdae61', '#ffffbf', '#abd9e9', '#2c7bb6')

#mapping interior condition - works

ggplot()+
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +
  geom_sf(data = seattleData, aes(colour =(conditionType)),
          show.legend = "point", size = .5) +
  scale_colour_manual(values = palette, name = "Condition Type") +
  labs(title = "Properties by Condition Type", 
       subtitle = "Seattle 2015")+
  theme_void()  

#mapping basement presence
ggplot()+
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +
  geom_sf(data = seattleData, aes(colour =(basementPresent)),
          show.legend = "point", size = .5) +
  scale_colour_manual(values = palette, name = "Basement Presence") +
  labs(title = "Properties by Basement Presence", 
       subtitle = "Seattle 2015")+
  theme_void()  

#mapping house size 
ggplot()+
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +
  geom_sf(data = seattleData, aes(colour =(houseSize)),
          show.legend = "point", size = .5) +
  scale_colour_manual(values = palette, name = "House Size") +
  labs(title = "Properties by Size", 
       subtitle = "Seattle 2015")+
  theme_void()  

## Mapping Spatial Variables

The map illustrates the distribution of properties around schools in Seattle for the year 2015, segmented into quintiles. Areas with a high concentration of properties in the top quintiles (red and orange) suggest neighborhoods with higher property values near schools, potentially indicating a desirability for educational proximity.

#spatial variables are schools, police stations, and transit stops

# Creating quintiles from the price variable
seattleData$priceQuintiles <- cut(seattleData$price, 
                                  breaks = quantile(seattleData$price, probs = seq(0, 1, by = 0.2)), 
                                  include.lowest = TRUE, 
                                  labels = FALSE)

# Converting the quintiles into a factor
seattleData$priceQuintiles <- factor(seattleData$priceQuintiles)

# Palette
palette <- c("#d7191c", "#fdae61", "#ffffbf", "#abdbe9", "#2c7bb6")

# Plot
ggplot() +
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +
  geom_sf(data = seattleData, aes(colour = priceQuintiles), size = 0.75, alpha = 0.3) + 
  scale_color_manual(values = palette, 
                     labels = c("Quintile 1", "Quintile 2", "Quintile 3", "Quintile 4", "Quintile 5")) +
  labs(title = "Properties around schools", subtitle = "Seattle 2015") +
  theme_void()

## Mapping Demographic Variables

This map represents the distribution of median household income around properties in Seattle for the year 2015. The color gradation reflects varying income levels, with darker shades indicating higher income brackets. Areas shaded in darker blue, for instance, suggest higher median incomes, which may correlate with more expensive properties or affluent neighborhoods.

#palette
palette <- c('#d7191c', '#fdae61', '#ffffbf', '#abd9e9', '#2c7bb6')

#mapping median income around properties
ggplot() +
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +  
  geom_sf(data = kcTracts_filtered, aes(fill = medIncome), color = "transparent", alpha = 0.5) +  
  scale_fill_gradientn(colors = palette) +
  labs(title = "Median Income Around Properties",
       subtitle = "Seattle 2015") +
  theme_void()

# Regression Model

Regression models are statistical methods used to predict the value of a dependent variable based on one or more independent variables, with training models built on known data for learning and test models applied to evaluate the prediction accuracy on unseen data.

Testing and Training Data

We are splitting the modelling data into training and testing sets, ensuring that the data is split randomly each time.

# Split the dataset into a training set and a test set using stratified sampling
inTrain <- createDataPartition(
              y = paste(seattleData$price, seattleData$pricePerFt2, seattleData$sqft_living, seattleData$condition, seattleData$bedrooms, seattleData$buildingAge, seattleData$dist2NearestPS, seattleData$dist2NearestSchool, seattleData$dist2NearestTransitStop, seattleData$medIncome, seattleData$PctWhite, seattleData$PctBlack, seattleData$PctHispanic, seattleData$PctPoverty, seattleData$PctBachelors), 
              p = .70, list = FALSE)  # Create a vector of indices for the training set, taking 70% of observations in the training dataset

# Subset the dataset to create the training set
seattle.training <- seattleData[inTrain,]  # Training set
# Subset the dataset to create the test set
seattle.test <- seattleData[-inTrain,]     # Test set

# Fitting a linear regression model to predict Sale Price using selected predictors
reg.training <- 
  lm(price ~ ., data = as.data.frame(seattle.training) %>% 
                             dplyr::select(price, pricePerFt2, sqft_living, condition, 
                                           bedrooms, buildingAge, dist2NearestPS, dist2NearestSchool, dist2NearestTransitStop, 
                                           medIncome, PctWhite, PctBlack, PctHispanic, PctPoverty, PctBachelors)) 
summary(reg.training)
## 
## Call:
## lm(formula = price ~ ., data = as.data.frame(seattle.training) %>% 
##     dplyr::select(price, pricePerFt2, sqft_living, condition, 
##         bedrooms, buildingAge, dist2NearestPS, dist2NearestSchool, 
##         dist2NearestTransitStop, medIncome, PctWhite, PctBlack, 
##         PctHispanic, PctPoverty, PctBachelors))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1319236   -36749     9211    44612  3082523 
## 
## Coefficients:
##                              Estimate    Std. Error t value
## (Intercept)             -593918.97406    6704.09904 -88.590
## pricePerFt2                1910.18144       6.25011 305.624
## sqft_living                 342.44773       0.84285 406.297
## condition                   883.19894     818.67316   1.079
## bedrooms                  -7844.99888     569.25939 -13.781
## buildingAge                 -44.11444      18.43487  -2.393
## dist2NearestPS           260679.58601   46594.99661   5.595
## dist2NearestSchool       -86033.24372   23493.09476  -3.662
## dist2NearestTransitStop      -4.01425       3.22056  -1.246
## medIncome                     0.21461       0.02394   8.966
## PctWhite                   -225.26706      63.62653  -3.540
## PctBlack                   -338.08453     124.75508  -2.710
## PctHispanic                 929.91315     104.29391   8.916
## PctPoverty                  -49.26588     140.29131  -0.351
## PctBachelors              -2145.72695     105.50078 -20.338
##                                     Pr(>|t|)    
## (Intercept)             < 0.0000000000000002 ***
## pricePerFt2             < 0.0000000000000002 ***
## sqft_living             < 0.0000000000000002 ***
## condition                            0.28067    
## bedrooms                < 0.0000000000000002 ***
## buildingAge                          0.01672 *  
## dist2NearestPS                  0.0000000222 ***
## dist2NearestSchool                   0.00025 ***
## dist2NearestTransitStop              0.21261    
## medIncome               < 0.0000000000000002 ***
## PctWhite                             0.00040 ***
## PctBlack                             0.00673 ** 
## PctHispanic             < 0.0000000000000002 ***
## PctPoverty                           0.72546    
## PctBachelors            < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 114000 on 47643 degrees of freedom
##   (238 observations deleted due to missingness)
## Multiple R-squared:  0.8936, Adjusted R-squared:  0.8935 
## F-statistic: 2.857e+04 on 14 and 47643 DF,  p-value: < 0.00000000000000022
## Plot regression 
#effect_plot(reg2, pred = number_of_bathrooms, interval = TRUE, plot.points = TRUE)
plot_summs(reg.training, scale = TRUE)

# Make predictions on the test set and evaluate model performance
seattle.test <-
  seattle.test %>%  # Pipe the test set into the following operations
  # Add a column indicating the type of regression model used
  mutate(Regression = "Baseline Regression",
         # Predict sale prices using the trained regression model
         SalePrice.Predict = predict(reg.training, seattle.test),
         # Calculate the difference between predicted and actual sale prices
         SalePrice.Error = SalePrice.Predict - price,
         # Calculate the absolute difference between predicted and actual sale prices
         SalePrice.AbsError = abs(SalePrice.Predict - price),
         # Calculate the absolute percentage error
         SalePrice.APE = (abs(SalePrice.Predict - price)) / price) %>%
  filter(price < 5000000)  # Filter out records with price greater than $5,000,000

The mean absolute error (MAE) for our model is currently approximately $64,798, and the Mean Absolute Percentage Error (MAPE) stands at around 17%. We experimented with various variable combinations to reduce these metrics, and we managed to achieve results close to the range of $50,000 to $100,000 (with a MAPE of 17%) by incorporating variables like “pricePerFt2”. Variables like price per square foot (pricePerFt2) and educational attainment (PctBachelors) are significant predictors, implying a strong relationship between these factors and housing prices.

mean(seattle.test$SalePrice.AbsError, na.rm = T) #MAE is the mean absolute error
## [1] 64798.57
mean(seattle.test$SalePrice.APE, na.rm = T)
## [1] 0.1709712

Cross validation

We used 100 folds for cross-validation. The model shows strong predictive power with an R-squared of 0.9, indicating that 90% of the variability in the housing prices can be explained by the model’s predictors. However, there is notable variation in the model’s performance across different cross-validation folds, as seen by the std deviation and average values in RMSE and MAE. The range of Mean Absolute Error (MAE) from around 57,980 to 78,327 highlights variability in prediction accuracy, which suggests that while the model explains much of the variance, its predictive performance could be inconsistent across different data samples. The Root Mean Square Error (RMSE) provides a sense of the magnitude of prediction errors. With an average RMSE of 112,359.1, the model’s predictions deviate from the actual values by this amount on average. The model may be effective for the dataset used, given the high R-squared value, but the RMSE suggests that the actual prediction errors could be substantial, affecting the model’s practical application in predicting housing prices.

seattle.test <-
  seattle.test %>%
  filter(price < 5000000)

# Set up cross-validation for model evaluation
fitControl <- trainControl(method = "cv", number = 100)

# Set the seed for reproducibility
set.seed(825) #seed makes sure that you get random numbers, so you do not get very different answers every time. This is done to make sure analysis is robust.

# Train a linear regression model using cross-validation
reg.cv <- 
  train(price ~ ., 
        data = st_drop_geometry(seattleData) %>% 
               dplyr::select(price, pricePerFt2, sqft_living, condition, 
                                           bedrooms, buildingAge, dist2NearestPS, dist2NearestSchool, dist2NearestTransitStop, 
                                           medIncome, PctWhite, PctBlack, PctHispanic, PctPoverty, PctBachelors), 
        method = "lm",  # Specify the modeling method as linear regression
        trControl = fitControl,  # Specify the cross-validation settings
        na.action = na.pass)  # Specify how to handle missing values

stargazer(as.data.frame(reg.cv$resample), type="text", digits=1, title="Cross Validation Results", out = "CV.txt") #all cv
## 
## Cross Validation Results
## ===================================================
## Statistic  N    Mean    St. Dev.   Min       Max   
## ---------------------------------------------------
## RMSE      100 112,359.1 18,263.0 89,048.0 176,096.0
## Rsquared  100    0.9      0.02     0.9       0.9   
## MAE       100 66,010.9  3,915.9  57,980.8 78,327.6 
## ---------------------------------------------------
# View the results of the cross-validated linear regression model
reg.cv
## Linear Regression 
## 
## 64080 samples
##    14 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (100 fold) 
## Summary of sample sizes: 63441, 63439, 63440, 63440, 63440, 63438, ... 
## Resampling results:
## 
##   RMSE      Rsquared   MAE     
##   112359.1  0.8974212  66010.95
## 
## Tuning parameter 'intercept' was held constant at a value of TRUE

Most of our MAE seem to be within the $57,000 to $80,000 range (with a mean of $66,000) which is illustrated in the following histogram.

#plotting the cross validation stuff

ggplot(reg.cv$resample, aes(x=MAE)) +
  geom_histogram(fill = "#2c7bb6") +
  labs(title = "Cross Validation Tests in Mean Average Error") +
  theme_minimal()

The histogram visualizes the distribution of the Mean Absolute Error (MAE) from cross-validation tests of the regression model. The majority of the MAE values cluster around the 65000 to 70000 range, indicating that the model’s prediction errors typically fall within this band. Fewer instances of the model exhibit significantly higher errors, with some outliers around 75000.

seattle.test %>%
  dplyr::select(SalePrice.Predict, price) %>%
    ggplot(aes(price, SalePrice.Predict)) +
  geom_point() +
  stat_smooth(aes(price, price), 
             method = "lm", se = FALSE, size = 1, colour="#d7191c") + 
  stat_smooth(aes(SalePrice.Predict, price), 
              method = "lm", se = FALSE, size = 1, colour="#2c7bb6") +
  labs(title="Predicted Sale Price as a Function of Observed Price",
       subtitle="Red line represents a perfect prediction; Blue line represents prediction",
       x = "Observed Price",
       y = "Predicted Price") +
  theme_minimal()+ xlim(0, 2000000) + ylim(0, 2000000)

The blue line, representing the model’s predictions, closely follows the red line, indicating that the model is performing well for many of the data points, particularly at lower price ranges. However, as the observed price increases, the predictions tend to deviate from the perfect line, showing some underestimation or overestimation by the model. The clustering of points along the blue line also suggests greater variability in predictions as the house price increases, which could be due to factors not captured by the model or the impact of higher-value outliers.

Spatial Correlations

In spatial correlation analysis, filtering for values greater than 0 can focus on areas where the prediction error indicates a consistent underestimation of property values, which might reveal spatial patterns or trends. This can help identify specific regions where the model’s performance is lacking due to possible local factors or spatial dependencies not captured in the model.

#use the same thing for weights and morans i 

# Spatial Lag for price
# Extract the coordinates from the 'seattleData' spatial dataframe
coords <- st_coordinates(seattleData) 
neighborList <- knn2nb(knearneigh(coords, 5))
spatialWeights <- nb2listw(neighborList, style="W")
seattleData$lagPrice <- lag.listw(spatialWeights, seattleData$price)

# Extract the coordinates of the test dataset
coords.test <- st_coordinates(seattle.test) #calculating spatial lag of errors to see if our model is misspecified

# Create a neighbor list using k-nearest neighbors (KNN) with k=5 for the test dataset
neighborList.test <- knn2nb(knearneigh(coords.test, 5))
# Convert the neighbor list to a spatial weights matrix for the test dataset
spatialWeights.test <- nb2listw(neighborList.test, style="W")

seattle.test$lagPrice <- lag.listw(spatialWeights.test, seattle.test$price)

seattle.test$lagPriceError <- lag.listw(spatialWeights.test, seattle.test$SalePrice.Error, NAOK = TRUE)

# Filtering greater than 0 values

seattle.test_filter <- seattle.test %>%
  filter(SalePrice.Error > 0, lagPriceError > 0)

ggplot(data = seattle.test_filter, aes(lagPriceError, SalePrice.Error)) +
  geom_point(size = .85,colour = "black") + 
  geom_smooth(method = "lm",colour = "red",size = 1.2) +
  labs(title="Price Errors") +
  theme_minimal()

The graph suggests that there is a positive relationship between sale price error and lag price error, indicating that neighborhoods with higher sale price predictions tend to also have neighboring areas with similar prediction errors.

Moran’s I

Moran’s I is a measure of spatial autocorrelation, meaning it tells us whether the pattern of a certain variable (like housing prices) is random or clustered across a geographic area. This suggests that there is no significant clustering of errors, a pattern that is also evident in the map. Consequently, it is probable that errors in our model may stem from other demographic or internal variables that we may not have accounted for. To improve the accuracy of our analysis, further investigation and inclusion of these potentially omitted variables might be necessary.

# for morans 1

# Spatial Lag for price
coords <- st_coordinates(seattle.test_filter) 
neighborList <- knn2nb(knearneigh(coords, 5))
spatialWeights <- nb2listw(neighborList, style="W")
seattle.test_filter$lagPrice <- lag.listw(spatialWeights, seattle.test_filter$price)

seattle.test_filter$lagPriceError <- lag.listw(spatialWeights, seattle.test_filter$SalePrice.Error, NAOK = TRUE)



moranTest <- moran.mc(na.omit(seattle.test_filter$SalePrice.Error),
                      spatialWeights, nsim = 999)  

ggplot(as.data.frame(moranTest$res[c(1:999)]), aes(moranTest$res[c(1:999)])) +
  geom_histogram(binwidth = 0.005) +
  geom_vline(aes(xintercept = moranTest$statistic), colour = "#d7191c",size=1) +
  scale_x_continuous(limits = c(-0.5,0.5)) +
  labs(title="Observed and permuted Moran's I",
       subtitle= "Observed Moran's I in red",
       x="Moran's I",
       y="Count") +
  theme_minimal()

The histogram shows the expected distribution of Moran’s I if there was no spatial autocorrelation, based on random permutations. The red line stands out on the right, suggesting the observed Moran’s I is significantly higher than what would be expected if there were no spatial pattern. This means that the variable being analyzed is not randomly distributed but, instead, is spatially clustered—neighboring areas are likely to have similar values.

Predictions by neighborhoods (using census tracts)

We are trying to assess how errors are distributed by neighborhoods (in this case, census tracts).

# Convert the 'seattle.test' dataset to a regular data frame
seattle.test %>%
  as.data.frame() %>%

  # Group the data frame by the 'TRACT.x' variable
  group_by(TRACT.x) %>%
  
  # Calculate the mean of 'SalePrice.Predict' and 'SalePrice' variables within each group
  summarize(meanPrediction = mean(SalePrice.Predict),
            meanPrice = mean(price)) %>%
  
  # Format the summarized data frame as an HTML table
  kable() %>%
  
  # Apply styling to enhance the appearance of the HTML table
  kable_styling()
TRACT.x meanPrediction meanPrice
000100 408396.5 412273.0
000200 455614.6 435950.0
000300 386338.2 388143.9
000401 495899.1 495161.1
000402 507514.8 507376.0
000500 687182.7 661347.0
000600 384418.5 389072.2
001200 386912.4 390688.0
001300 490248.7 484662.9
001400 480903.1 487999.6
001500 642996.8 621617.1
001600 607865.7 588014.3
001701 481826.6 473885.2
001702 542028.3 535987.6
001800 615803.4 599850.9
001900 483361.8 482372.4
002700 608407.7 595790.8
002800 593094.3 583963.9
002900 611281.1 594322.2
003200 636217.2 609013.9
003300 622431.9 581122.6
003400 612525.2 600736.8
003500 608806.5 586739.3
003600 574679.3 558455.0
004100 844035.1 829986.7
004200 851709.7 871522.8
004301 949268.5 975664.5
004302 765597.2 736649.1
004400 959381.9 984070.9
004500 682901.9 672742.7
004600 708752.6 693552.4
004700 593587.4 556556.1
004800 606356.0 593047.2
004900 593758.6 576996.9
005000 594657.1 586358.8
005100 670051.5 661225.2
005200 629665.5 616741.9
005301 918062.8 924991.7
005302 770062.7 762283.3
005400 653737.7 649910.8
005600 747574.6 729768.9
005700 846099.3 848519.1
005801 766564.0 728406.9
005802 884284.6 860121.5
006000 801552.2 803461.5
006100 943774.1 975929.8
006200 994527.9 1077813.9
006300 1140166.3 1231542.3
006400 997393.9 1056110.0
006500 926467.2 965677.4
006600 844714.2 862680.0
006700 862169.2 886832.3
006800 856992.2 907942.9
007000 870329.3 875688.6
007100 875535.4 909261.9
007200 803389.7 787635.2
007300 883930.6 922821.2
007401 832335.9 852402.1
007402 724870.0 701701.4
007500 967267.2 1010869.7
007600 1045993.4 1098221.6
007700 1025071.7 1077597.8
007800 NA 788339.8
008001 917542.2 944048.0
008900 601689.1 596845.6
009000 NA 535274.4
009100 NA 590712.0
009300 564423.8 557867.1
009400 NA 613868.2
009500 NA 556950.2
009900 295241.8 316194.0
010001 NA 513216.3
010002 590506.3 596202.1
010100 NA 522958.2
010300 NA 331494.8
010401 NA 368135.9
010402 NA 352543.6
010500 612886.1 600914.6
010600 594679.2 594630.6
010701 323077.8 326578.1
010800 302975.9 316000.2
010900 NA 369658.6
011001 NA 358692.5
011002 NA 373160.8
011200 NA 348052.2
011300 NA 335767.8
011401 316696.3 328247.0
011402 316880.7 319770.0
011500 NA 542428.8
011600 559453.5 544531.2
011700 NA 322258.2
011900 286875.9 298848.9
012000 426077.8 427345.1
012100 430088.0 423636.0
020100 697313.3 673145.2
020200 474660.2 472187.6
020300 394008.5 395403.1
020401 429304.8 411798.3
020402 433415.7 421201.3
020500 424039.1 422788.5
020600 389114.6 392086.4
020700 376172.3 385195.3
020800 479249.5 479535.4
020900 476539.6 478707.4
021000 395940.6 395076.5
021100 441742.7 454439.7
021300 464069.9 446132.1
021400 408206.5 425368.8
021500 452796.9 458409.8
025302 294087.9 293206.9
026001 314717.9 314298.3
026002 364007.6 353038.4
026100 288441.2 301148.1
026200 263599.5 270045.9
026300 NA 304962.9
026400 NA 282187.4
026500 NA 312658.5
026600 283887.1 304919.6
026700 405626.1 407822.0
026801 271963.6 284599.6
026802 284854.8 300743.9
027000 207912.1 234381.5
027100 230445.2 249655.2
027200 261838.3 259760.2
027300 238187.9 248090.7
027400 273473.3 262514.2
027500 313622.3 330425.3
027600 408501.2 390377.8
027800 443406.1 415567.1
027900 327809.2 331005.1
028000 219655.5 244000.6
028100 242268.1 256504.5
028200 209190.7 242897.5
028300 NA 311186.8
028402 280741.7 280661.3
028403 288540.7 277701.9
028500 317727.6 302086.8
028600 NA 405907.3
028700 NA 292581.7
028801 NA 312876.0
028802 NA 299605.8
028901 NA 281782.5
028902 NA 284013.2
029001 NA 268994.0
029003 NA 341979.8
029004 NA 315470.2
029101 NA 329347.8
030003 NA 301543.6
030100 NA 282832.9

The table shows that the model’s predictions for housing prices by census tract are reasonably close to the actual mean prices, suggesting a good model fit for the tracts.

Regression with neighborhood effects

Let’s try to run the regression again, but this time with a neighborhood fixed effect. We do this by simply adding the variable ‘TRACT.x’ which is the census tract to the regression model as a neighborhood-level dummy variable.

# This code fits a linear regression model ('reg.nhood') to predict 'SalePrice' using various predictors, including neighborhood-related variables, using the training dataset.

# Fit a linear regression model to the training dataset ('boston.training') 
reg.nhood <- lm(price ~ ., #adding dummy variable for name
                data = as.data.frame(seattle.training) %>% 
                         dplyr::select(TRACT.x, price, pricePerFt2, sqft_living, condition, 
                                           bedrooms, buildingAge, dist2NearestPS, dist2NearestSchool, dist2NearestTransitStop,
                                           medIncome, PctWhite, PctBlack, PctHispanic, PctPoverty, PctBachelors))
#View the model stats
summary(reg.nhood)
## 
## Call:
## lm(formula = price ~ ., data = as.data.frame(seattle.training) %>% 
##     dplyr::select(TRACT.x, price, pricePerFt2, sqft_living, condition, 
##         bedrooms, buildingAge, dist2NearestPS, dist2NearestSchool, 
##         dist2NearestTransitStop, medIncome, PctWhite, PctBlack, 
##         PctHispanic, PctPoverty, PctBachelors))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1294060   -37422    11284    45273  3089251 
## 
## Coefficients:
##                              Estimate    Std. Error t value
## (Intercept)             -587768.43258    9688.91031 -60.664
## TRACT.x000200              7497.82983    8746.97058   0.857
## TRACT.x000300             12166.16949    8743.37409   1.391
## TRACT.x000401              2163.37137    7927.91809   0.273
## TRACT.x000402              1932.95743    7956.12161   0.243
## TRACT.x000500             -7343.94131   10641.82080  -0.690
## TRACT.x000600             11091.87196    8869.56425   1.251
## TRACT.x001200             11403.81362    8759.67422   1.302
## TRACT.x001300             -2035.88546    7493.84125  -0.272
## TRACT.x001400              -441.25693    7898.16523  -0.056
## TRACT.x001500            -10203.70048   10362.78131  -0.985
## TRACT.x001600            -11409.56976   10368.42922  -1.100
## TRACT.x001701             -1196.63958    7508.02690  -0.159
## TRACT.x001702             -4739.17665    7274.40730  -0.651
## TRACT.x001800            -11932.07988    8376.47042  -1.424
## TRACT.x001900             -3570.30428    7484.16599  -0.477
## TRACT.x002700            -13188.63745    8358.68880  -1.578
## TRACT.x002800            -14292.73324    8352.25569  -1.711
## TRACT.x002900            -11693.11229    8330.26234  -1.404
## TRACT.x003200            -40450.83615    9897.58854  -4.087
## TRACT.x003300            -37653.75172   10042.43058  -3.749
## TRACT.x003400            -23554.12225    7753.63308  -3.038
## TRACT.x003500            -20284.66536    7786.14326  -2.605
## TRACT.x003600            -11812.63656    8303.63656  -1.423
## TRACT.x004100             16663.58785   10847.31437   1.536
## TRACT.x004200              4152.85460   10894.41387   0.381
## TRACT.x004301              4346.02930   10594.09535   0.410
## TRACT.x004302             21895.66749   10852.50405   2.018
## TRACT.x004400              1578.83690   10905.23313   0.145
## TRACT.x004500             -6046.42985    7883.19374  -0.767
## TRACT.x004600             -4610.63033    7817.51365  -0.590
## TRACT.x004700            -38707.51015   10069.53026  -3.844
## TRACT.x004800            -23162.50274    7768.08120  -2.982
## TRACT.x004900            -11538.67725    8408.14190  -1.372
## TRACT.x005000            -14093.59619    8240.03469  -1.710
## TRACT.x005100             -6522.36405    7837.47921  -0.832
## TRACT.x005200             -4800.81499    7858.52396  -0.611
## TRACT.x005301              8717.20030   10892.99011   0.800
## TRACT.x005302             14671.13736   10800.91943   1.358
## TRACT.x005400             -7957.50530    7832.58971  -1.016
## TRACT.x005600            -24413.15588   10100.50497  -2.417
## TRACT.x005700            -31948.14418   10014.81964  -3.190
## TRACT.x005801            -18948.22314    9853.42604  -1.923
## TRACT.x005802            -23063.15213    9932.91888  -2.322
## TRACT.x006000             33379.40523   13858.45909   2.409
## TRACT.x006100             72809.16302    9338.36068   7.797
## TRACT.x006200             45993.06457    9337.45354   4.926
## TRACT.x006300             66553.89507    9960.07822   6.682
## TRACT.x006400             73207.55065   10013.93562   7.311
## TRACT.x006500             60005.77517    9386.28574   6.393
## TRACT.x006600             41639.49000   11175.22490   3.726
## TRACT.x006700             26929.06002   14337.21519   1.878
## TRACT.x006800             14578.30620   14631.62823   0.996
## TRACT.x007000             31834.50682   13729.70312   2.319
## TRACT.x007100             25446.01960   13668.16331   1.862
## TRACT.x007200             37349.48677   13731.76427   2.720
## TRACT.x007300             22601.58455   13979.91846   1.617
## TRACT.x007401             52138.00631   14170.40803   3.679
## TRACT.x007402             61710.96552   13981.14468   4.414
## TRACT.x007500             68710.59324    9242.42223   7.434
## TRACT.x007600             75111.24406   10150.40542   7.400
## TRACT.x007700             76134.76020   10305.60430   7.388
## TRACT.x007800             36192.22584    8470.38246   4.273
## TRACT.x008001             26367.13154   13917.70559   1.895
## TRACT.x008900              1924.17400    9819.36029   0.196
## TRACT.x009000              4414.09836    9857.44903   0.448
## TRACT.x009100              2768.56341    9548.54299   0.290
## TRACT.x009300             -4874.01094    8679.22617  -0.562
## TRACT.x009400               167.86165    9901.74969   0.017
## TRACT.x009500              1768.98398    9820.39006   0.180
## TRACT.x009900             16632.61843    9533.24700   1.745
## TRACT.x010001             -3649.57012    8814.96699  -0.414
## TRACT.x010002             -2836.76629    9964.74677  -0.285
## TRACT.x010100             -8034.87066    8813.43348  -0.912
## TRACT.x010300            -20097.83744   12126.43715  -1.657
## TRACT.x010401            -14333.51586   11817.79684  -1.213
## TRACT.x010402             -9117.05304   11930.47518  -0.764
## TRACT.x010500            -12353.53333    9948.45263  -1.242
## TRACT.x010600            -15079.65043   10081.28864  -1.496
## TRACT.x010701             21786.61389    9501.29754   2.293
## TRACT.x010800             18868.14921    9451.31018   1.996
## TRACT.x010900            -16073.72141   11945.75835  -1.346
## TRACT.x011001             -6331.80543   12125.89013  -0.522
## TRACT.x011002            -14235.69075   11904.38256  -1.196
## TRACT.x011200             11216.50478    8605.31232   1.303
## TRACT.x011300              9696.82743    8621.20152   1.125
## TRACT.x011401             19375.43260    9422.35924   2.056
## TRACT.x011402             22152.63229    9625.75141   2.301
## TRACT.x011500            -12479.12852    9946.61917  -1.255
## TRACT.x011600            -12025.47879    9948.20976  -1.209
## TRACT.x011700             -1574.14519    9090.87612  -0.173
## TRACT.x011900              5257.72629   10433.04208   0.504
## TRACT.x012000              2438.57439    8357.95538   0.292
## TRACT.x012100              4925.49121    8320.32679   0.592
## TRACT.x020100             -9896.67126   10278.35946  -0.963
## TRACT.x020200              3002.42543    7948.13724   0.378
## TRACT.x020300              6793.79280    7580.89216   0.896
## TRACT.x020401              6671.78824    8715.83357   0.765
## TRACT.x020402              5875.16636    8818.18117   0.666
## TRACT.x020500              1998.32237    8667.18138   0.231
## TRACT.x020600              6087.46471    7602.37338   0.801
## TRACT.x020700              9101.65472    8670.35970   1.050
## TRACT.x020800              1526.50496    8022.46097   0.190
## TRACT.x020900              1178.54606    7911.63219   0.149
## TRACT.x021000              7783.03576    7609.82431   1.023
## TRACT.x021100             -2755.93033    8772.58360  -0.314
## TRACT.x021300              7948.53051    8859.42072   0.897
## TRACT.x021400             -4699.46215    8845.42803  -0.531
## TRACT.x021500              -540.17423    8792.10231  -0.061
## TRACT.x025302              9823.13388   10272.87997   0.956
## TRACT.x026001              9171.97694   10524.95666   0.871
## TRACT.x026002             12519.53909   10366.22100   1.208
## TRACT.x026100              5332.08679   10335.23482   0.516
## TRACT.x026200             19581.48426    8250.17309   2.373
## TRACT.x026300             15391.05711    8130.76031   1.893
## TRACT.x026400             20204.21451    8893.83683   2.272
## TRACT.x026500             13597.80259    7512.06119   1.810
## TRACT.x026600             15944.06787    8136.72426   1.960
## TRACT.x026700             19481.73014    9759.73370   1.996
## TRACT.x026801             27018.84564    8465.87589   3.192
## TRACT.x026802             25959.96548    8457.60218   3.069
## TRACT.x027000             33988.75967   10198.16140   3.333
## TRACT.x027100             35889.40921   10143.78570   3.538
## TRACT.x027200             42301.47230   10229.56225   4.135
## TRACT.x027300             39201.42459   10319.93026   3.799
## TRACT.x027400             43887.45810   10100.07547   4.345
## TRACT.x027500             11939.13334    7854.18627   1.520
## TRACT.x027600             10538.66810    8411.29149   1.253
## TRACT.x027800             -4096.35047   10141.65538  -0.404
## TRACT.x027900             16248.34592    8355.67215   1.945
## TRACT.x028000             32221.42194    9769.24185   3.298
## TRACT.x028100             25460.40832    9067.79997   2.808
## TRACT.x028200             19418.47481    9183.56587   2.114
## TRACT.x028300             28482.07469    9442.25383   3.016
## TRACT.x028402             12616.44810   11447.19068   1.102
## TRACT.x028403              8724.99811   12666.16774   0.689
## TRACT.x028500             16651.57647   11637.56396   1.431
## TRACT.x028600             13841.39964    8576.50899   1.614
## TRACT.x028700             27088.38690   10364.27100   2.614
## TRACT.x028801             23746.64851    9155.01250   2.594
## TRACT.x028802             24992.89726    9498.50409   2.631
## TRACT.x028901             20342.48814   10695.79518   1.902
## TRACT.x028902             31763.67550   10860.25952   2.925
## TRACT.x029001             23655.11311   10627.77825   2.226
## TRACT.x029003             29504.42954   10655.20134   2.769
## TRACT.x029004             31274.82437   10665.39045   2.932
## TRACT.x029101             31773.03458   10729.76725   2.961
## TRACT.x030003             32682.71714   10771.80852   3.034
## TRACT.x030100             23662.68895   10777.81762   2.195
## pricePerFt2                1879.16700       6.84914 274.365
## sqft_living                 337.88209       0.86112 392.376
## condition                  2549.84391     815.74246   3.126
## bedrooms                  -7314.94129     565.58353 -12.933
## buildingAge                 -72.04554      18.39781  -3.916
## dist2NearestPS           598634.16099   59734.83411  10.022
## dist2NearestSchool      -245105.13298   42928.50873  -5.710
## dist2NearestTransitStop       0.43600       3.25772   0.134
## medIncome                     0.11202       0.02556   4.382
## PctWhite                   -269.33630      71.29642  -3.778
## PctBlack                   -651.23568     136.65018  -4.766
## PctHispanic                 450.75459     122.80427   3.671
## PctPoverty                 -103.84779     146.47740  -0.709
## PctBachelors              -1549.06101     119.17955 -12.998
##                                     Pr(>|t|)    
## (Intercept)             < 0.0000000000000002 ***
## TRACT.x000200                       0.391343    
## TRACT.x000300                       0.164089    
## TRACT.x000401                       0.784947    
## TRACT.x000402                       0.808043    
## TRACT.x000500                       0.490133    
## TRACT.x000600                       0.211103    
## TRACT.x001200                       0.192973    
## TRACT.x001300                       0.785874    
## TRACT.x001400                       0.955447    
## TRACT.x001500                       0.324802    
## TRACT.x001600                       0.271157    
## TRACT.x001701                       0.873369    
## TRACT.x001702                       0.514736    
## TRACT.x001800                       0.154315    
## TRACT.x001900                       0.633330    
## TRACT.x002700                       0.114610    
## TRACT.x002800                       0.087043 .  
## TRACT.x002900                       0.160417    
## TRACT.x003200            0.00004378204798116 ***
## TRACT.x003300                       0.000177 ***
## TRACT.x003400                       0.002384 ** 
## TRACT.x003500                       0.009184 ** 
## TRACT.x003600                       0.154863    
## TRACT.x004100                       0.124497    
## TRACT.x004200                       0.703063    
## TRACT.x004301                       0.681638    
## TRACT.x004302                       0.043642 *  
## TRACT.x004400                       0.884887    
## TRACT.x004500                       0.443084    
## TRACT.x004600                       0.555339    
## TRACT.x004700                       0.000121 ***
## TRACT.x004800                       0.002867 ** 
## TRACT.x004900                       0.169970    
## TRACT.x005000                       0.087202 .  
## TRACT.x005100                       0.405299    
## TRACT.x005200                       0.541265    
## TRACT.x005301                       0.423565    
## TRACT.x005302                       0.174368    
## TRACT.x005400                       0.309659    
## TRACT.x005600                       0.015652 *  
## TRACT.x005700                       0.001423 ** 
## TRACT.x005801                       0.054485 .  
## TRACT.x005802                       0.020243 *  
## TRACT.x006000                       0.016018 *  
## TRACT.x006100            0.00000000000000648 ***
## TRACT.x006200            0.00000084360735197 ***
## TRACT.x006300            0.00000000002381923 ***
## TRACT.x006400            0.00000000000027019 ***
## TRACT.x006500            0.00000000016425353 ***
## TRACT.x006600                       0.000195 ***
## TRACT.x006700                       0.060351 .  
## TRACT.x006800                       0.319082    
## TRACT.x007000                       0.020418 *  
## TRACT.x007100                       0.062652 .  
## TRACT.x007200                       0.006532 ** 
## TRACT.x007300                       0.105946    
## TRACT.x007401                       0.000234 ***
## TRACT.x007402            0.00001017620927941 ***
## TRACT.x007500            0.00000000000010692 ***
## TRACT.x007600            0.00000000000013861 ***
## TRACT.x007700            0.00000000000015183 ***
## TRACT.x007800            0.00001934114154838 ***
## TRACT.x008001                       0.058164 .  
## TRACT.x008900                       0.844645    
## TRACT.x009000                       0.654305    
## TRACT.x009100                       0.771859    
## TRACT.x009300                       0.574410    
## TRACT.x009400                       0.986474    
## TRACT.x009500                       0.857048    
## TRACT.x009900                       0.081044 .  
## TRACT.x010001                       0.678862    
## TRACT.x010002                       0.775890    
## TRACT.x010100                       0.361951    
## TRACT.x010300                       0.097454 .  
## TRACT.x010401                       0.225183    
## TRACT.x010402                       0.444763    
## TRACT.x010500                       0.214333    
## TRACT.x010600                       0.134711    
## TRACT.x010701                       0.021852 *  
## TRACT.x010800                       0.045901 *  
## TRACT.x010900                       0.178451    
## TRACT.x011001                       0.601553    
## TRACT.x011002                       0.231766    
## TRACT.x011200                       0.192431    
## TRACT.x011300                       0.260694    
## TRACT.x011401                       0.039757 *  
## TRACT.x011402                       0.021374 *  
## TRACT.x011500                       0.209627    
## TRACT.x011600                       0.226743    
## TRACT.x011700                       0.862529    
## TRACT.x011900                       0.614299    
## TRACT.x012000                       0.770466    
## TRACT.x012100                       0.553865    
## TRACT.x020100                       0.335620    
## TRACT.x020200                       0.705616    
## TRACT.x020300                       0.370165    
## TRACT.x020401                       0.443990    
## TRACT.x020402                       0.505251    
## TRACT.x020500                       0.817656    
## TRACT.x020600                       0.423291    
## TRACT.x020700                       0.293841    
## TRACT.x020800                       0.849091    
## TRACT.x020900                       0.881583    
## TRACT.x021000                       0.306426    
## TRACT.x021100                       0.753406    
## TRACT.x021300                       0.369625    
## TRACT.x021400                       0.595222    
## TRACT.x021500                       0.951010    
## TRACT.x025302                       0.338966    
## TRACT.x026001                       0.383513    
## TRACT.x026002                       0.227159    
## TRACT.x026100                       0.605917    
## TRACT.x026200                       0.017626 *  
## TRACT.x026300                       0.058372 .  
## TRACT.x026400                       0.023109 *  
## TRACT.x026500                       0.070282 .  
## TRACT.x026600                       0.050058 .  
## TRACT.x026700                       0.045925 *  
## TRACT.x026801                       0.001416 ** 
## TRACT.x026802                       0.002146 ** 
## TRACT.x027000                       0.000860 ***
## TRACT.x027100                       0.000403 ***
## TRACT.x027200            0.00003552262591508 ***
## TRACT.x027300                       0.000146 ***
## TRACT.x027400            0.00001393989436685 ***
## TRACT.x027500                       0.128493    
## TRACT.x027600                       0.210241    
## TRACT.x027800                       0.686278    
## TRACT.x027900                       0.051830 .  
## TRACT.x028000                       0.000974 ***
## TRACT.x028100                       0.004990 ** 
## TRACT.x028200                       0.034479 *  
## TRACT.x028300                       0.002559 ** 
## TRACT.x028402                       0.270405    
## TRACT.x028403                       0.490926    
## TRACT.x028500                       0.152481    
## TRACT.x028600                       0.106562    
## TRACT.x028700                       0.008961 ** 
## TRACT.x028801                       0.009494 ** 
## TRACT.x028802                       0.008510 ** 
## TRACT.x028901                       0.057188 .  
## TRACT.x028902                       0.003449 ** 
## TRACT.x029001                       0.026033 *  
## TRACT.x029003                       0.005625 ** 
## TRACT.x029004                       0.003366 ** 
## TRACT.x029101                       0.003066 ** 
## TRACT.x030003                       0.002414 ** 
## TRACT.x030100                       0.028133 *  
## pricePerFt2             < 0.0000000000000002 ***
## sqft_living             < 0.0000000000000002 ***
## condition                           0.001774 ** 
## bedrooms                < 0.0000000000000002 ***
## buildingAge              0.00009016173913804 ***
## dist2NearestPS          < 0.0000000000000002 ***
## dist2NearestSchool       0.00000001139074530 ***
## dist2NearestTransitStop             0.893533    
## medIncome                0.00001180032790292 ***
## PctWhite                            0.000158 ***
## PctBlack                 0.00000188741787196 ***
## PctHispanic                         0.000242 ***
## PctPoverty                          0.478348    
## PctBachelors            < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 112800 on 47495 degrees of freedom
##   (238 observations deleted due to missingness)
## Multiple R-squared:  0.8962, Adjusted R-squared:  0.8959 
## F-statistic:  2532 on 162 and 47495 DF,  p-value: < 0.00000000000000022
#r squared went up to 92% when neighbourhood was taken into consideration

# Create a new dataset ('seattle.test.nhood') by predicting 'price' for the test dataset ('seattle.test') using the neighborhood effects model ('reg.nhood')
seattle.test.nhood <- #doing exactly the same thing, but for this new model now
  seattle.test %>%
  mutate(Regression = "Neighborhood Effects",  # Add a new variable indicating the type of regression model
         SalePrice.Predict = predict(reg.nhood, seattle.test),  # Predict 'SalePrice' using the fitted model
         SalePrice.Error = SalePrice.Predict - price,  # Calculate the error between predicted and actual 'SalePrice'
         SalePrice.AbsError = abs(SalePrice.Predict - price),  # Calculate the absolute error
         SalePrice.APE = (abs(SalePrice.Predict - price)) / price) %>%  # Calculate the absolute percentage error
  filter(price < 5000000)  # Filter out observations with 'SalePrice' greater than $5,000,000

The regression with neighborhood effects demonstrates that accounting for neighborhood-level characteristics can impact the model’s predictive power, as indicated by the high R-squared value.

Residuals

The map aims to depict average residuals by census tracts to assess the model’s prediction errors across different areas of Seattle. However, due to a visualization issue, the map currently shows all areas as black, indicating a problem with the scaling or classification of the residuals into different color ranges,which we were not able to resolve, thus preventing us from drawing any accurate inferences about the spatial distribution of residuals.

coords <- st_coordinates(seattleData) 
neighborList <- knn2nb(knearneigh(coords, 5))
spatialWeights <- nb2listw(neighborList, style="W")
seattleData$lagPrice <- lag.listw(spatialWeights, seattleData$price)

# Extract the coordinates of the test dataset
coords.test <- st_coordinates(seattle.test) #calculating spatial lag of errors to see if our model is misspecified

# Create a neighbor list using k-nearest neighbors (KNN) with k=5 for the test dataset
neighborList.test <- knn2nb(knearneigh(coords.test, 5))
# Convert the neighbor list to a spatial weights matrix for the test dataset
spatialWeights.test <- nb2listw(neighborList.test, style="W")

seattle.test$lagPrice <- lag.listw(spatialWeights.test, seattle.test$price)

seattle.test$lagPriceError <- lag.listw(spatialWeights.test, seattle.test$SalePrice.Error, NAOK = TRUE)

seattle.test <- seattle.test %>%
  mutate(Residual = price - SalePrice.Predict) %>%
  group_by(TRACT.x) %>%
  summarise(AvgResidual = mean(Residual, na.rm = TRUE))

# Ensure that kcTracts_filtered is an sf object and has the correct CRS
kcTracts_filtered <- st_as_sf(kcTracts_filtered)
kcTracts_filtered <- st_set_crs(kcTracts_filtered, st_crs(seattle.test))

# Perform the spatial join
seattle_residuals <- st_join(seattle.test, kcTracts_filtered)

# Create the color palette for the gradient
color_palette <- colorRampPalette(colors = c("#d7191c", "#fdae61", "#ffffbf", "#abd9e9", "#2c7bb6"))

# Generate a sequence of colors from the palette
palette <- color_palette(100)  # This will create a smooth gradient with 100 colors

# Plot the kcTracts_filtered as the base layer in grey
ggplot() +
  geom_sf(data = kcTracts_filtered, fill = "grey89") +  # Base layer
  geom_sf(data = seattle_residuals, aes(fill = AvgResidual), size = 0.5) +  # Residuals layer
  scale_fill_gradientn(colors = palette) +  # Gradient scale for residuals
  labs(title = "Average Residuals by Census Tracts", fill = "Avg Residual") +
  theme_void()

Conclusion

From this analysis, one can infer that housing prices in Seattle are influenced by a combination of property characteristics, demographic factors, and proximity to amenities, and there is variability in how well the model’s predictions align with actual sale prices across different areas. This suggests that while the model captures broad trends, local factors and potential data issues may cause variations in prediction accuracy, which would be important for stakeholders to consider.

  • The regression models suggest that variables like square footage and demographic factors have significant relationships with housing prices, indicating that larger, newer homes in areas with higher median incomes tend to fetch higher prices.
  • The map showing properties by sale price reveals a clear spatial pattern in property values, with some areas consistently showcasing higher-valued properties, potentially reflecting neighborhood desirability or other location-specific advantages.
  • The presence of basements seems to be a common feature in certain areas, which may correspond to the architectural style or age of the housing stock in those neighborhoods.
  • Proximity to schools appears to be a factor in housing prices, as seen in the quintile distribution around educational institutions, suggesting that homes near schools may be in higher demand, affecting their market value.
  • Demographic variables, like median income, shown through mapping, reflect economic disparities across different areas, which likely influence housing affordability and investment patterns.
  • The attempt to visualize average residuals by census tract aimed to assess prediction errors geographically. However, the visualization challenges prevented a clear understanding of spatial patterns in model accuracy.
---
title: "Predicting Housing Prices in Seattle"
author: "Kamya Khandelwal, Revathi Machan"
date: "`r Sys.Date()`"
output:
  html_document:
    toc: true
    toc_float: true
    code_folding: hide
    code_download: true
    theme: journal  
---

#Setting up 

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  echo = TRUE,
  message = FALSE,
  warning = FALSE,
  cache = TRUE)
```

Property Value Prediction Model 
- predictive model of price incorporating structural and locational characteristics 
- summary statistics w variable descriptions
- correlation matrix
- 4 home price correlation scatterplots
- 1 map of dep variable (sale price)
- 3 maps of 3 most interesting independent variables (factors we choose)
- testing and training dataset???
- discussion of performance
- plot of predicted prices as function of observed prices
- map of residuals 

# Introduction 

The Seattle housing market is a vibrant and complex sector that encapsulates the city's economic growth and diverse population. Seattle offers a mix of modern high-rise apartments, classic craftsman houses, and waterfront properties, which serve the varied preferences of its residents. The housing prices in Seattle are shaped by an array of factors, including location, architectural style, age of the property, and proximity to amenities like parks, schools, and public transport.

This project evaluates factors affecting housing prices to create an accurate and generalizable OLS regression model to predict them. Housing prices in Seattle have been subject to fluctuations over the years, influenced by various factors such as the neighborhood, property type, and home condition. Sale prediction algorithms are crucial tools that help different stakeholders in the housing market make informed decisions, identify inequalities, and ensure the real estate market's overall health and fairness. 

Building a predictive model for property valuation is challenging, requiring selecting the right features, addressing collinearity among variables, choosing appropriate modeling techniques, and ensuring interpretability. Creating this model was an iterative process that involved multiple rounds of trial and error, particularly in attempts to minimize the errors in predictions. The maps, correlation matrix, and scatterplots illustrate various variables that were considered, wrangled, and filtered as part of the data analysis process.


```{r setting up the packages}
if (!require(pacman)){install.packages("pacman"); library(pacman)}
p_load (sf, tidyverse, knitr, kableExtra, rmarkdown, tidycensus, dplyr, scales, stringr, ggcorrplot, readxl, data.table, caTools, tmap, stargazer, spdep, caret, ckanr, FNN, grid, gridExtra, jtools, broom, tufte, rmarkdown, brewer.pal, ggplot2)
```

```{r api}
census_api_key("b3eda1fa84dde3c5ad443fd407d48f2584ab2726", overwrite = TRUE)
```

# Data Wrangling

Census, OpenData Seattle and provided Dataset 

## Provided Dataset and Internal Variables

The code below is used to import the foundational dataset for our model. This dataset contains information on home sales prices and property characteristics in Seattle, Kings County for the years 2014 and 2015. The model we are developing is designed to make predictions about home prices and utilizes specific property attributes from this dataset to enhance the accuracy of those predictions.

```{r Reading Data 1, results= 'hide'}

kingsCounty <- read.csv("kc_house_data.csv")
kingsCoSF <- st_as_sf(kingsCounty, coords = c("long", "lat"), crs = 4326)

seattleTreeCanopy <- read.csv("Seattle_Tree_Canopy_2016_2021_RSE_Census_Tracts.csv")

crs <- st_crs(kingsCoSF)
print(crs)

```
Getting census tracts data from HUD USPS Crosswalk files to assign census tracts to the original data.

```{r Reading Data 2, results= 'hide'}

#Data from HUD USPS Zipcode Crosswalk files
hud_data <- read_excel("ZIP_TRACT_032015.xlsx")

desired_zips <- c("98101", "98102", "98103", "98104", "98105", "98106", "98107", "98108", 
                  "98109", "98111", "98112", "98113", "98114", "98115", "98116", "98117", 
                  "98118", "98119", "98120", "98121", "98122", "98123", "98124", "98125", 
                  "98126", "98131", "98132", "98133", "98134", "98135", "98136", "98138", 
                  "98144", "98145", "98146", "98148", "98154", "98155", "98158", "98160", 
                  "98161", "98164", "98166", "98168", "98171", "98174", "98177", "98178", 
                  "98188", "98198", "98199")

```

```{r filtering data}
#filtering out data that's not Seattle

seattleData <- kingsCoSF %>%
  filter(zipcode %in% c("98101","98102","98103","98104","98105", "98106","98107", "98108","98109","98111","98112","98113",'98114","98115"."98116","98117","98118","98119","98120","98121","98122","98123","98124","98125","98126","98131","98132',"98133","98134","98135","98136","98138","98144","98145","98146","98148","98154","98155","98158","98160","98161","98164","98166","98168","98171","98174","98177","98178","98188","98198","98199"))

seattleData$zipcode <- as.character(seattleData$zipcode)
hud_data$ZIP <- as.character(hud_data$ZIP)

#Filtering HUD data for zipcodes of interest
hud_data_filtered <- hud_data[hud_data$ZIP %in% desired_zips, ]

#Merging the filtered HUD dataset with the seattle housing data
seattleData <- merge(seattleData, hud_data_filtered, by.x = "zipcode", by.y = "ZIP", all.x = TRUE)

#removing extra columns
seattleData <- seattleData %>%
  select(-OTH_RATIO, -RES_RATIO, -TOT_RATIO, -BUS_RATIO)

seattleData <- seattleData %>%
  mutate(TRACT = str_sub(TRACT, -6)) # Keep the last 6 characters


seattleData <- seattleData %>%
  filter(yr_built > 0) 

#categorizing based on basement presence
seattleData <- seattleData %>%
  mutate(basementPresent = case_when(
    sqft_basement == 0 ~ 'No Basement',
    sqft_basement >= 1 ~ 'Basement'))

#categorizing based on condition
seattleData <- seattleData %>%
  mutate(conditionType  = case_when(
    condition == '1' ~ 'Very Poor',
    condition == '2' ~ 'Poor',
    condition == '3' ~ 'Average',
    condition == '4' ~ 'Good',
    condition == '5' ~ 'Very Good'))

seattleData <- seattleData %>%
  mutate(houseSize = case_when(
    sqft_living >= 2000 ~ 'Big',
    sqft_living <= 1999 ~ 'Small'))

seattleDisability <- seattleTreeCanopy %>%
  select(PCT_ADULT_WITH_DISABILITIES)


#summary statistics should ideally combine the different datasets 
summary(seattleData)

```

```{r impute missing data}

seattleData <- seattleData %>%
  mutate(bedroomIndex = case_when(
    bedrooms >= 1 ~ 1, 
    bedrooms < 1 ~ 0))

seattleData$bedroomIndex[is.na(seattleData$bedroomIndex)] <- 0

lm(bedrooms ~ sqft_living, data = seattleData)
for(i in 1:nrow(seattleData))
{
  if(seattleData$bedroomIndex[i] == 0)
  {seattleData$bedrooms[i] = 1.9054627 +  0.0007142*seattleData$sqft_living}
}

seattleData$bedrooms <- round(seattleData$bedrooms, digits = 0)


```

```{r creating new variables}

seattleData <- seattleData %>%
  mutate(pricePerFt2 = (price/sqft_living)) #might need to do the linear regression bathroom and rooms for this stuff

seattleData <- seattleData %>%
  mutate(buildingAge = (2015 -(yr_built)))
```

## Census Data Collection

The census information from 2021 offers a detailed look at the community and housing in King County, including stuff like how many people live there, what types of homes they have, and income levels. To use this data with housing prices from 2015, we need to remember that things might have changed over those six years, which could affect the home prices in Seattle.

```{r census data}
acsVariables2015 <- load_variables(2015, "acs5", cache = TRUE)

# 2021, A

# Retrieve ACS data for Seattle tracts in 2015
kcTracts <- get_acs(
  geography = "tract",
  variables = c(
    "B01003_001",   # Total Population
    "B19013_001",   # Median Household Income
    "B25058_001",   # Median Rent
    "B25008_002",   # Owner-Occupied Units
    "B25008_003",   # Renter-Occupied Units
    "B07001_032",   # Same House 75 Years Ago
    "B07001_017",   # Same House 1 Year Ago
    "B25088_003",   # Median Selected Monthly Owner Costs (homes without a mortgage)
    "B25088_002",   # Median Selected Monthly Owner Costs (homes with a mortgage)
    "B15003_022",   # Educational Attainment: Bachelor's Degree
    "B17001_002",   # Percentage of Population Below the Poverty Level
    "B28002_004",   # Percentage of Housing Units with High-Speed Internet
    "B25044_003",   # Percentage of Housing Units with No Vehicle Available
    "B02001_002",   # Race and Ethnicity: White Alone
    "B02001_003",   # Race and Ethnicity: Black or African American Alone
    "B03001_003"    # Hispanic or Latino Origin of Population
  ),
  year = 2021,
  state = "WA",#washington
  county = "King",#kings county
  geometry = TRUE,
  output = "wide"
)%>%
  select(-NAME, -ends_with("M")) %>%
  rename(totalPop = B01003_001E,                           # Total Population
         medIncome = B19013_001E,                         # Median Household Income
         medRent = B25058_001E,                           # Median Rent
         ownerUnits = B25008_002E,                        # Owner-Occupied Units
         renterUnits = B25008_003E,                       # Renter-Occupied Units
         sameHouse75 = B07001_032E,                      # Same House 75 Years Ago
         sameHouse1 = B07001_017E,                       # Same House 1 Year Ago
         medianNoMortgage = B25088_003E,          # Median Selected Monthly Owner Costs (homes without a mortgage)
         medianMortgage = B25088_002E,        # Median Selected Monthly Owner Costs (homes with a mortgage)
         bachelors = B15003_022E,                      # Educational Attainment: Bachelor's Degree
         belowPoverty = B17001_002E,                  # Percentage of Population Below the Poverty Level
         highSpeedInternet = B28002_004E,  # Percentage of Housing Units with High-Speed Internet
         noVehicle = B25044_003E,           # Percentage of Housing Units with No Vehicle Available
         White = B02001_002E,                         # Race and Ethnicity: White Alone
         Black = B02001_003E,                         # Race and Ethnicity: Black or African American Alone
         hispanicLatino = B03001_003E                     # Race and Ethnicity: Hispanic or Latino
         )

# Transform the data to ESRI:102728 projection
kcTracts <- kcTracts %>% st_transform(st_crs(seattleData)) #need to add projection to kc stuff earlier

#also need to filter out the tracts for seattle!!!! 

```

```{r spatial variables}
seattleSchools <- read.csv("Seattle_Public_Schools_Sites_2023-2024.csv")
seattleSchools <- st_as_sf(seattleSchools, coords = c("Longitude", "Latitude"), crs = 4326) %>%
  st_transform(st_crs(seattleData))

#mapping nearest school
closestSchool <- sf::st_nearest_feature(seattleData, seattleSchools)

#converting into rsgeo geometries
x <- rsgeo::as_rsgeo(seattleData)
y <- rsgeo::as_rsgeo(seattleSchools)

## Calculating distance
seattleData$dist2NearestSchool <- rsgeo::distance_euclidean_pairwise(x, y[closestSchool])

#Police Stations
kcPS <- read.csv("Police_Station_Locations_in_King_County___kcp_loc_point.csv")

seattlePS <- kcPS %>%
  filter(ZIPCODE %in% c("98101","98102","98103","98104","98105", "98106","98107", "98108","98109","98111","98112","98113",'98114","98115"."98116","98117","98118","98119","98120","98121","98122","98123","98124","98125","98126","98131","98132',"98133","98134","98135","98136","98138","98144","98145","98146","98148","98154","98155","98158","98160","98161","98164","98166","98168","98171","98174","98177","98178","98188","98198","98199"))

kcPS <- st_as_sf(seattlePS, coords = c("X", "Y"), crs = 4326) %>%
  st_transform(st_crs(seattleData))



# Checking CRS of seattleData and seattlePS
crs_seattleData <- st_crs(seattleData)
crs_seattlePS <- st_crs(seattlePS)

print(crs_seattleData)
print(crs_seattlePS)

# Checking class of the datasets and ensuring crs is same
print(class(seattleData))
print(class(seattlePS))

if (!inherits(seattlePS, "sf")) {
  seattlePS <- st_as_sf(seattlePS, coords = c("X", "Y"), crs = 4326)
}

# Transforming seattlePS to match the crs of seattleData
if (!st_crs(seattleData) == st_crs(seattlePS)) {
  seattlePS <- st_transform(seattlePS, st_crs(seattleData))
}

#mapping nearest police stations
closestPS <- sf::st_nearest_feature(seattleData, seattlePS)

#converting into rsgeo geometries
x <- rsgeo::as_rsgeo(seattleData)
y <- rsgeo::as_rsgeo(seattlePS)

#calculating distance
seattleData$dist2NearestPS <- rsgeo::distance_euclidean_pairwise(x,y[closestPS])

#Transit Stops
kcTransitStops <- read.csv("Transit_Stops_for_King_County_Metro___transitstop_point.csv")

seattleTransitStops <- kcTransitStops %>%
  filter(ZIPCODE %in% c("98101","98102","98103","98104","98105", "98106","98107", "98108","98109","98111","98112","98113",'98114","98115"."98116","98117","98118","98119","98120","98121","98122","98123","98124","98125","98126","98131","98132',"98133","98134","98135","98136","98138","98144","98145","98146","98148","98154","98155","98158","98160","98161","98164","98166","98168","98171","98174","98177","98178","98188","98198","98199"))

kcTransitStops <- st_as_sf(seattleTransitStops, coords = c("X", "Y"), crs = 4326) %>%
  st_transform(st_crs(seattleData))

kcTransitStops <- st_transform(kcTransitStops, st_crs(seattleData))

closestTransitStop <- st_nearest_feature(seattleData, kcTransitStops)

seattleData$dist2NearestTransitStop <- st_distance(seattleData, kcTransitStops[closestTransitStop,], by_element = TRUE)

# converting it to character
seattleData$dist2NearestTransitStop <- as.character(seattleData$dist2NearestTransitStop)

# removing '[m]' from the string
seattleData$dist2NearestTransitStop <- sub("\\s\\[m\\]", "", seattleData$dist2NearestTransitStop)

# converting the results back to numeric
seattleData$dist2NearestTransitStop <- as.numeric(seattleData$dist2NearestTransitStop)


```

```{r pop, warning=FALSE, results='hide'}

kcTracts <- kcTracts %>%
  mutate(PctWhite = ((White/totalPop)*100),
         PctBlack = ((Black/totalPop)*100),
         PctHispanic = ((hispanicLatino/totalPop)*100),
         PctBachelors = ((bachelors/totalPop)*100),
         PctPoverty = ((belowPoverty/totalPop)*100))

# Filter kctracts to include only the specified GEOID range
kcTracts_filtered <- kcTracts %>%
  filter(as.numeric(GEOID) >= 53033000100 & as.numeric(GEOID) <= 53033030100)

#removing extra columns
kcTracts_filtered <- kcTracts_filtered %>%
  select(-medRent, -ownerUnits, -renterUnits, -sameHouse75, -sameHouse1, -medianNoMortgage, -medianMortgage, -bachelors, -belowPoverty, -highSpeedInternet, -noVehicle, -Black, -White, -hispanicLatino, -totalPop, -geometry)

# Check the result
head(kcTracts_filtered)

```


```{r merge, warning=FALSE, results='hide'}

kcTracts_filtered <- kcTracts_filtered %>%
  rename(TRACT = GEOID) %>% # Rename GEOID to TRACT
  mutate(TRACT = str_sub(TRACT, -6)) # Keep the last 6 characters


# Joining data from two datasets
seattleData <- st_join(seattleData, kcTracts_filtered)
```

# Summary Statistics

Summary statistics provide a quick snapshot of key attributes of your dataset, such as the average values, variability, and distribution across different variables, which can indicate trends and outliers in your data. They're essential for understanding the general behavior of the dataset before diving into deeper analysis.

## Summary Statistics: Internal Variables

These statistics provide an overview of the central tendency, spread, and range of the internal variables for Seattle homes, which include prices, price per square foot, living area size, year built, number of rooms etc.

```{r summ stat int}
InternalVariables <- seattleData

InternalVariables <- st_drop_geometry(InternalVariables)

InternalVariables <- InternalVariables %>%
  dplyr::select("price", "pricePerFt2", "sqft_living", "yr_built", "bedrooms", "bathrooms", "condition", "sqft_basement", "sqft_lot")

stargazer(as.data.frame(InternalVariables), type="text", digits=1, title = "Descriptive Statistics for Seattle Homes Internal Variables", out = "Training_seattleInternal.txt")
```
It is observed that the average sale price of homes in Seattle is approximately 502,782.6 USD. The sale prices vary quite widely with a high standard deviation, indicating a more heterogenous market. 

The average age for a house in Seattle is approximately 65 years indicating a large share of the market is held by homes constructed a long time ago.

## Summary Statistics: Demographic Variables

These statistics provide an overview of the central tendency, spread, and range of the internal variables for Seattle homes, which include median income, percentage of white population, percentage of black population, percentage of hispanic population, percentage of population with a bachelor's degree and percentage of population living in poverty.

```{r summ stat dem}
DemographicVariables <- seattleData

DemographicVariables <- st_drop_geometry(DemographicVariables)

DemographicVariables <- DemographicVariables %>%
  dplyr::select("PctWhite", "PctBlack", "PctHispanic", "PctBachelors", "PctPoverty", "medIncome") 

stargazer(as.data.frame(DemographicVariables), type="text", digits=1, title = "Descriptive Statistics for Seattle Homes Demographic Variables", out = "Training_seattleSpatial.txt")
```
The table presents descriptive statistics for demographic variables related to Seattle homes, offering insights into the characteristics of the population in different areas.

On average, approximately 63.6% of the population in the observed areas is White. The range of White population percentages spans from 7.3% to 93.1%, indicating a wide diversity in racial composition across different areas of Seattle. The same does not hold true for Black and Hispanic population percentages indicating the presence of White-majority neighborhoods in different parts of Seattle.

The average median household income in the observed areas is $108,185.2 with approximately 8.4% of the population in the observed areas falls below the poverty level, on average.

## Summary Statistics: Spatial Variables

These statistics provide an overview of the central tendency, spread, and range of the internal variables for Seattle homes, which include distances to key nearest amenities.

```{r summ stat spat}

SpatialVariables <- seattleData 

SpatialVariables <- st_drop_geometry(SpatialVariables)

SpatialVariables <- SpatialVariables %>%
  dplyr::select("dist2NearestSchool", "dist2NearestPS", "dist2NearestTransitStop") 

stargazer(as.data.frame(SpatialVariables), type="text", digits=1, title = "Descriptive Statistics for Seattle Homes Spatial Variables (Figure 4.1)", out = "Training_seattleSpatial.txt")

```
These statistics offer insights into the spatial characteristics of Seattle neighborhoods where the "Mean" in each case represents the average distance to a specific amenity like police stations, schools and transit stops from a listed property. 

# Scatterplots 

The following code generates a set of scatterplots to explore the relationships between the sale price of homes and various continuous variables.  The data is first filtered to exclude observations where the sale_price is less than 5,000,000 to remove any outliers. For the remaining data, a set of scatterplots is created. The scatterplots help visualize the relationships between the sale price of homes and each of the continuous variables, as well as the direction and strength of these relationships. The regression lines indicate whether there is a linear trend in the data.

```{r scatterplots, fig.align="center", warning=FALSE, echo = FALSE, fig.width = 14, fig.height=28 }
options(scipen = 9999) #turns off scientific notation and how many points

Variable <- seattleData %>%
  filter(price < 5000000)

## Scatterplot
st_drop_geometry(Variable) %>% 
  dplyr::select(price, sqft_living, yr_built, medIncome, PctWhite, PctBachelors, dist2NearestTransitStop) %>% 
  filter(price < 5000000) %>%
  gather(Variable, Value, -price) %>% 
   ggplot(aes(Value, price)) +
     geom_point(size = .5) + geom_smooth(method = "lm", se=F, colour = "#FA7800") +
     facet_wrap(~Variable, ncol = 2, scales = "free") +
     labs(title = "Price as a function of continuous variables") +
     theme_minimal()
```

The scatterplots illustrate that in Seattle, home prices have a positive relationship with square footage and percentage of residents with a bachelor's degree, suggesting larger homes and more educated neighborhoods tend to have higher property values. Conversely, there's no clear pattern with the age of the house, indicating that newer does not necessarily mean more expensive in this market.

# Correlation Matrix

The correlation matrix provides a numerical summary of how different variables in the housing dataset are related to one another. The correlation matrix indicates that home prices in the Seattle housing dataset are positively correlated with the size of the living area and the number of bathrooms, meaning larger homes and those with more bathrooms tend to be more expensive. There seems to be a slight negative correlation between the price of homes and the distance to the nearest public school and transit stop, implying that homes closer to schools may command higher prices. The zeros in the correlation matrix highlight that there is no linear relationship between the home price and the year built or between the distances to nearest public school and transit stops, which stands out, suggesting that newer homes are not necessarily priced higher and that proximity to these amenities does not uniformly affect home values.

```{r corr}
int_variables <- c("price", "condition", "sqft_living", "yr_built", "bedrooms", "bathrooms", "dist2NearestSchool", "dist2NearestPS", "dist2NearestTransitStop", "PctWhite", "PctBachelors", "medIncome")

seattleDatacorr <- seattleData %>% 
  st_drop_geometry() %>% 
  select(all_of(int_variables)) %>% 
  na.omit()

corr <- cor(seattleDatacorr)
rounded_corr <- round(corr, 1)
ggcorrplot(rounded_corr,
           type = "lower",
           lab = TRUE,
           lab_size = 2,
           colors = c("#d7191c", "#ffffbf", "#2c7bb6"),
           title = "Correlation Matrix of Housing Dataset",
           ggtheme = theme_bw())
```

# Exploratory Mapping and analysis

```{r mapping}

#making a function for the quintile breaks
qBr <- function(data, var_name) {
  # Extract the variable from the dataframe
  var <- data[[var_name]]
  # Calculate quintiles
  quintiles <- quantile(var, probs = seq(0, 1, by = 0.25), na.rm = TRUE)
  # Return breaks
  return(quintiles)
}

#function for map theme

mapTheme <- function() {
  tm_shape() +
    tm_layout(
      # Customize map background and frame
      background.color = "lightblue",
      frame = FALSE,
      
      # Customize text style and color
      title.text.size = 1.2,
      text.color = "darkblue",
      
      # Customize legend appearance
      legend.position = c("right", "bottom"),
      legend.bg.color = "lightgray",
      legend.text.size = 0.8,
      legend.title.size = 0.9,
      
      # Add more customizations as needed
    )
}

```

## Mapping sale price

```{r map int sp}

# Creating quintiles from the price variable
seattleData$priceQuintiles <- cut(seattleData$price, 
                                  breaks = quantile(seattleData$price, probs = seq(0, 1, by = 0.2)), 
                                  include.lowest = TRUE, 
                                  labels = FALSE)

# Converting the quintiles into a factor
seattleData$priceQuintiles <- factor(seattleData$priceQuintiles)

#palette
palette <- c('#d7191c', '#fdae61', '#ffffbf', '#abd9e9', '#2c7bb6')

#mapping sale price
ggplot() +
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +
  geom_sf(data = seattleData, aes(colour = priceQuintiles)) +  # Ensure q5(price) is a factor
  scale_color_manual(values = palette,  # Use scale_color_manual to match the color aesthetic
                     labels = qBr(seattleData, "price"),
                     name = "Quintile Breaks:\nSale Price") +  # Correct label text
  labs(title = "Properties by Sale Price", subtitle = "Seattle 2015") +
  theme_void()
```
The map shows the distribution of property sale prices across Seattle in 2015, with areas color-coded by quintile to indicate the range of sale prices. Red indicates the lowest price quintile while blue represents the highest, illustrating the spatial patterns of housing affordability or value within the city. This could reflect various socioeconomic factors, urban development patterns, and housing demand in different neighborhoods.

## Mapping internal variables

The maps visualize the spatial distribution of basements, property conditions and property size across Seattle's residential properties in 2015. 

```{r map int}

#palette
palette <- c('#d7191c', '#fdae61', '#ffffbf', '#abd9e9', '#2c7bb6')

#mapping interior condition - works

ggplot()+
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +
  geom_sf(data = seattleData, aes(colour =(conditionType)),
          show.legend = "point", size = .5) +
  scale_colour_manual(values = palette, name = "Condition Type") +
  labs(title = "Properties by Condition Type", 
       subtitle = "Seattle 2015")+
  theme_void()  

#mapping basement presence
ggplot()+
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +
  geom_sf(data = seattleData, aes(colour =(basementPresent)),
          show.legend = "point", size = .5) +
  scale_colour_manual(values = palette, name = "Basement Presence") +
  labs(title = "Properties by Basement Presence", 
       subtitle = "Seattle 2015")+
  theme_void()  

#mapping house size 
ggplot()+
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +
  geom_sf(data = seattleData, aes(colour =(houseSize)),
          show.legend = "point", size = .5) +
  scale_colour_manual(values = palette, name = "House Size") +
  labs(title = "Properties by Size", 
       subtitle = "Seattle 2015")+
  theme_void()  

```
## Mapping Spatial Variables

The map illustrates the distribution of properties around schools in Seattle for the year 2015, segmented into quintiles. Areas with a high concentration of properties in the top quintiles (red and orange) suggest neighborhoods with higher property values near schools, potentially indicating a desirability for educational proximity.

```{r map spat var}

#spatial variables are schools, police stations, and transit stops

# Creating quintiles from the price variable
seattleData$priceQuintiles <- cut(seattleData$price, 
                                  breaks = quantile(seattleData$price, probs = seq(0, 1, by = 0.2)), 
                                  include.lowest = TRUE, 
                                  labels = FALSE)

# Converting the quintiles into a factor
seattleData$priceQuintiles <- factor(seattleData$priceQuintiles)

# Palette
palette <- c("#d7191c", "#fdae61", "#ffffbf", "#abdbe9", "#2c7bb6")

# Plot
ggplot() +
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +
  geom_sf(data = seattleData, aes(colour = priceQuintiles), size = 0.75, alpha = 0.3) + 
  scale_color_manual(values = palette, 
                     labels = c("Quintile 1", "Quintile 2", "Quintile 3", "Quintile 4", "Quintile 5")) +
  labs(title = "Properties around schools", subtitle = "Seattle 2015") +
  theme_void()

```
## Mapping Demographic Variables

This map represents the distribution of median household income around properties in Seattle for the year 2015. The color gradation reflects varying income levels, with darker shades indicating higher income brackets. Areas shaded in darker blue, for instance, suggest higher median incomes, which may correlate with more expensive properties or affluent neighborhoods. 

```{r map dem var}

#palette
palette <- c('#d7191c', '#fdae61', '#ffffbf', '#abd9e9', '#2c7bb6')

#mapping median income around properties
ggplot() +
  geom_sf(data = kcTracts_filtered, fill = "grey89", color = "darkgrey") +  
  geom_sf(data = kcTracts_filtered, aes(fill = medIncome), color = "transparent", alpha = 0.5) +  
  scale_fill_gradientn(colors = palette) +
  labs(title = "Median Income Around Properties",
       subtitle = "Seattle 2015") +
  theme_void()

```
# Regression Model

Regression models are statistical methods used to predict the value of a dependent variable based on one or more independent variables, with training models built on known data for learning and test models applied to evaluate the prediction accuracy on unseen data.

## Testing and Training Data 

We are splitting the modelling data into training and testing sets, ensuring that the data is split randomly each time.

```{r train data}

# Split the dataset into a training set and a test set using stratified sampling
inTrain <- createDataPartition(
              y = paste(seattleData$price, seattleData$pricePerFt2, seattleData$sqft_living, seattleData$condition, seattleData$bedrooms, seattleData$buildingAge, seattleData$dist2NearestPS, seattleData$dist2NearestSchool, seattleData$dist2NearestTransitStop, seattleData$medIncome, seattleData$PctWhite, seattleData$PctBlack, seattleData$PctHispanic, seattleData$PctPoverty, seattleData$PctBachelors), 
              p = .70, list = FALSE)  # Create a vector of indices for the training set, taking 70% of observations in the training dataset

# Subset the dataset to create the training set
seattle.training <- seattleData[inTrain,]  # Training set
# Subset the dataset to create the test set
seattle.test <- seattleData[-inTrain,]     # Test set

# Fitting a linear regression model to predict Sale Price using selected predictors
reg.training <- 
  lm(price ~ ., data = as.data.frame(seattle.training) %>% 
                             dplyr::select(price, pricePerFt2, sqft_living, condition, 
                                           bedrooms, buildingAge, dist2NearestPS, dist2NearestSchool, dist2NearestTransitStop, 
                                           medIncome, PctWhite, PctBlack, PctHispanic, PctPoverty, PctBachelors)) 
summary(reg.training)

## Plot regression 
#effect_plot(reg2, pred = number_of_bathrooms, interval = TRUE, plot.points = TRUE)
plot_summs(reg.training, scale = TRUE)

# Make predictions on the test set and evaluate model performance
seattle.test <-
  seattle.test %>%  # Pipe the test set into the following operations
  # Add a column indicating the type of regression model used
  mutate(Regression = "Baseline Regression",
         # Predict sale prices using the trained regression model
         SalePrice.Predict = predict(reg.training, seattle.test),
         # Calculate the difference between predicted and actual sale prices
         SalePrice.Error = SalePrice.Predict - price,
         # Calculate the absolute difference between predicted and actual sale prices
         SalePrice.AbsError = abs(SalePrice.Predict - price),
         # Calculate the absolute percentage error
         SalePrice.APE = (abs(SalePrice.Predict - price)) / price) %>%
  filter(price < 5000000)  # Filter out records with price greater than $5,000,000

```
The mean absolute error (MAE) for our model is currently approximately `$64,798`, and the Mean Absolute Percentage Error (MAPE) stands at around 17%. We experimented with various variable combinations to reduce these metrics, and we managed to achieve results close to the range of $50,000 to $100,000 (with a MAPE of 17%) by incorporating variables like "pricePerFt2". Variables like price per square foot (pricePerFt2) and educational attainment (PctBachelors) are significant predictors, implying a strong relationship between these factors and housing prices.

```{r mean}
mean(seattle.test$SalePrice.AbsError, na.rm = T) #MAE is the mean absolute error
mean(seattle.test$SalePrice.APE, na.rm = T)
```

# Cross validation

We used 100 folds for cross-validation. The model shows strong predictive power with an R-squared of 0.9, indicating that 90% of the variability in the housing prices can be explained by the model's predictors. However, there is notable variation in the model's performance across different cross-validation folds, as seen by the std deviation and average values in RMSE and MAE. The range of Mean Absolute Error (MAE) from around 57,980 to 78,327 highlights variability in prediction accuracy, which suggests that while the model explains much of the variance, its predictive performance could be inconsistent across different data samples. The Root Mean Square Error (RMSE) provides a sense of the magnitude of prediction errors. With an average RMSE of 112,359.1, the model's predictions deviate from the actual values by this amount on average. The model may be effective for the dataset used, given the high R-squared value, but the RMSE suggests that the actual prediction errors could be substantial, affecting the model's practical application in predicting housing prices.

```{r crossvalidation}

seattle.test <-
  seattle.test %>%
  filter(price < 5000000)

# Set up cross-validation for model evaluation
fitControl <- trainControl(method = "cv", number = 100)

# Set the seed for reproducibility
set.seed(825) #seed makes sure that you get random numbers, so you do not get very different answers every time. This is done to make sure analysis is robust.

# Train a linear regression model using cross-validation
reg.cv <- 
  train(price ~ ., 
        data = st_drop_geometry(seattleData) %>% 
               dplyr::select(price, pricePerFt2, sqft_living, condition, 
                                           bedrooms, buildingAge, dist2NearestPS, dist2NearestSchool, dist2NearestTransitStop, 
                                           medIncome, PctWhite, PctBlack, PctHispanic, PctPoverty, PctBachelors), 
        method = "lm",  # Specify the modeling method as linear regression
        trControl = fitControl,  # Specify the cross-validation settings
        na.action = na.pass)  # Specify how to handle missing values

stargazer(as.data.frame(reg.cv$resample), type="text", digits=1, title="Cross Validation Results", out = "CV.txt") #all cv

# View the results of the cross-validated linear regression model
reg.cv

```
Most of our MAE seem to be within the $57,000 to $80,000 range (with a mean of $66,000) which is illustrated in the following histogram.  

```{r plot cv}
#plotting the cross validation stuff

ggplot(reg.cv$resample, aes(x=MAE)) +
  geom_histogram(fill = "#2c7bb6") +
  labs(title = "Cross Validation Tests in Mean Average Error") +
  theme_minimal()

```
The histogram visualizes the distribution of the Mean Absolute Error (MAE) from cross-validation tests of the regression model. The majority of the MAE values cluster around the 65000 to 70000 range, indicating that the model's prediction errors typically fall within this band. Fewer instances of the model exhibit significantly higher errors, with some outliers around 75000.

```{r predict sp}

seattle.test %>%
  dplyr::select(SalePrice.Predict, price) %>%
    ggplot(aes(price, SalePrice.Predict)) +
  geom_point() +
  stat_smooth(aes(price, price), 
             method = "lm", se = FALSE, size = 1, colour="#d7191c") + 
  stat_smooth(aes(SalePrice.Predict, price), 
              method = "lm", se = FALSE, size = 1, colour="#2c7bb6") +
  labs(title="Predicted Sale Price as a Function of Observed Price",
       subtitle="Red line represents a perfect prediction; Blue line represents prediction",
       x = "Observed Price",
       y = "Predicted Price") +
  theme_minimal()+ xlim(0, 2000000) + ylim(0, 2000000)
```

The blue line, representing the model’s predictions, closely follows the red line, indicating that the model is performing well for many of the data points, particularly at lower price ranges. However, as the observed price increases, the predictions tend to deviate from the perfect line, showing some underestimation or overestimation by the model. The clustering of points along the blue line also suggests greater variability in predictions as the house price increases, which could be due to factors not captured by the model or the impact of higher-value outliers.

# Spatial Correlations 

In spatial correlation analysis, filtering for values greater than 0 can focus on areas where the prediction error indicates a consistent underestimation of property values, which might reveal spatial patterns or trends. This can help identify specific regions where the model’s performance is lacking due to possible local factors or spatial dependencies not captured in the model.

```{r spat correlation}

#use the same thing for weights and morans i 

# Spatial Lag for price
# Extract the coordinates from the 'seattleData' spatial dataframe
coords <- st_coordinates(seattleData) 
neighborList <- knn2nb(knearneigh(coords, 5))
spatialWeights <- nb2listw(neighborList, style="W")
seattleData$lagPrice <- lag.listw(spatialWeights, seattleData$price)

# Extract the coordinates of the test dataset
coords.test <- st_coordinates(seattle.test) #calculating spatial lag of errors to see if our model is misspecified

# Create a neighbor list using k-nearest neighbors (KNN) with k=5 for the test dataset
neighborList.test <- knn2nb(knearneigh(coords.test, 5))
# Convert the neighbor list to a spatial weights matrix for the test dataset
spatialWeights.test <- nb2listw(neighborList.test, style="W")

seattle.test$lagPrice <- lag.listw(spatialWeights.test, seattle.test$price)

seattle.test$lagPriceError <- lag.listw(spatialWeights.test, seattle.test$SalePrice.Error, NAOK = TRUE)

# Filtering greater than 0 values

seattle.test_filter <- seattle.test %>%
  filter(SalePrice.Error > 0, lagPriceError > 0)

ggplot(data = seattle.test_filter, aes(lagPriceError, SalePrice.Error)) +
  geom_point(size = .85,colour = "black") + 
  geom_smooth(method = "lm",colour = "red",size = 1.2) +
  labs(title="Price Errors") +
  theme_minimal()


```
The graph suggests that there is a positive relationship between sale price error and lag price error, indicating that neighborhoods with higher sale price predictions tend to also have neighboring areas with similar prediction errors.

## Moran's I 

Moran's I is a measure of spatial autocorrelation, meaning it tells us whether the pattern of a certain variable (like housing prices) is random or clustered across a geographic area. This suggests that there is no significant clustering of errors, a pattern that is also evident in the map. Consequently, it is probable that errors in our model may stem from other demographic or internal variables that we may not have accounted for. To improve the accuracy of our analysis, further investigation and inclusion of these potentially omitted variables might be necessary.

```{r morans i}

# for morans 1

# Spatial Lag for price
coords <- st_coordinates(seattle.test_filter) 
neighborList <- knn2nb(knearneigh(coords, 5))
spatialWeights <- nb2listw(neighborList, style="W")
seattle.test_filter$lagPrice <- lag.listw(spatialWeights, seattle.test_filter$price)

seattle.test_filter$lagPriceError <- lag.listw(spatialWeights, seattle.test_filter$SalePrice.Error, NAOK = TRUE)



moranTest <- moran.mc(na.omit(seattle.test_filter$SalePrice.Error),
                      spatialWeights, nsim = 999)  

ggplot(as.data.frame(moranTest$res[c(1:999)]), aes(moranTest$res[c(1:999)])) +
  geom_histogram(binwidth = 0.005) +
  geom_vline(aes(xintercept = moranTest$statistic), colour = "#d7191c",size=1) +
  scale_x_continuous(limits = c(-0.5,0.5)) +
  labs(title="Observed and permuted Moran's I",
       subtitle= "Observed Moran's I in red",
       x="Moran's I",
       y="Count") +
  theme_minimal()
```

The histogram shows the expected distribution of Moran's I if there was no spatial autocorrelation, based on random permutations. The red line stands out on the right, suggesting the observed Moran's I is significantly higher than what would be expected if there were no spatial pattern. This means that the variable being analyzed is not randomly distributed but, instead, is spatially clustered—neighboring areas are likely to have similar values.

## Predictions by neighborhoods (using census tracts)

We are trying to assess how errors are distributed by neighborhoods (in this case, census tracts).

```{r predictbytracts}

# Convert the 'seattle.test' dataset to a regular data frame
seattle.test %>%
  as.data.frame() %>%

  # Group the data frame by the 'TRACT.x' variable
  group_by(TRACT.x) %>%
  
  # Calculate the mean of 'SalePrice.Predict' and 'SalePrice' variables within each group
  summarize(meanPrediction = mean(SalePrice.Predict),
            meanPrice = mean(price)) %>%
  
  # Format the summarized data frame as an HTML table
  kable() %>%
  
  # Apply styling to enhance the appearance of the HTML table
  kable_styling()

```

The table shows that the model's predictions for housing prices by census tract are reasonably close to the actual mean prices, suggesting a good model fit for the tracts.

## Regression with neighborhood effects

Let's try to run the regression again, but this time with a neighborhood fixed effect. We do this by simply adding the variable 'TRACT.x' which is the census tract to the regression model as a neighborhood-level dummy variable.

```{r nbd}
# This code fits a linear regression model ('reg.nhood') to predict 'SalePrice' using various predictors, including neighborhood-related variables, using the training dataset.

# Fit a linear regression model to the training dataset ('boston.training') 
reg.nhood <- lm(price ~ ., #adding dummy variable for name
                data = as.data.frame(seattle.training) %>% 
                         dplyr::select(TRACT.x, price, pricePerFt2, sqft_living, condition, 
                                           bedrooms, buildingAge, dist2NearestPS, dist2NearestSchool, dist2NearestTransitStop,
                                           medIncome, PctWhite, PctBlack, PctHispanic, PctPoverty, PctBachelors))
#View the model stats
summary(reg.nhood)
#r squared went up to 92% when neighbourhood was taken into consideration

# Create a new dataset ('seattle.test.nhood') by predicting 'price' for the test dataset ('seattle.test') using the neighborhood effects model ('reg.nhood')
seattle.test.nhood <- #doing exactly the same thing, but for this new model now
  seattle.test %>%
  mutate(Regression = "Neighborhood Effects",  # Add a new variable indicating the type of regression model
         SalePrice.Predict = predict(reg.nhood, seattle.test),  # Predict 'SalePrice' using the fitted model
         SalePrice.Error = SalePrice.Predict - price,  # Calculate the error between predicted and actual 'SalePrice'
         SalePrice.AbsError = abs(SalePrice.Predict - price),  # Calculate the absolute error
         SalePrice.APE = (abs(SalePrice.Predict - price)) / price) %>%  # Calculate the absolute percentage error
  filter(price < 5000000)  # Filter out observations with 'SalePrice' greater than $5,000,000

```
The regression with neighborhood effects demonstrates that accounting for neighborhood-level characteristics can impact the model's predictive power, as indicated by the high R-squared value.

# Residuals

The map aims to depict average residuals by census tracts to assess the model's prediction errors across different areas of Seattle. However, due to a visualization issue, the map currently shows all areas as black, indicating a problem with the scaling or classification of the residuals into different color ranges,which we were not able to resolve, thus preventing us from drawing any accurate inferences about the spatial distribution of residuals.

```{r residual}

coords <- st_coordinates(seattleData) 
neighborList <- knn2nb(knearneigh(coords, 5))
spatialWeights <- nb2listw(neighborList, style="W")
seattleData$lagPrice <- lag.listw(spatialWeights, seattleData$price)

# Extract the coordinates of the test dataset
coords.test <- st_coordinates(seattle.test) #calculating spatial lag of errors to see if our model is misspecified

# Create a neighbor list using k-nearest neighbors (KNN) with k=5 for the test dataset
neighborList.test <- knn2nb(knearneigh(coords.test, 5))
# Convert the neighbor list to a spatial weights matrix for the test dataset
spatialWeights.test <- nb2listw(neighborList.test, style="W")

seattle.test$lagPrice <- lag.listw(spatialWeights.test, seattle.test$price)

seattle.test$lagPriceError <- lag.listw(spatialWeights.test, seattle.test$SalePrice.Error, NAOK = TRUE)

seattle.test <- seattle.test %>%
  mutate(Residual = price - SalePrice.Predict) %>%
  group_by(TRACT.x) %>%
  summarise(AvgResidual = mean(Residual, na.rm = TRUE))

# Ensure that kcTracts_filtered is an sf object and has the correct CRS
kcTracts_filtered <- st_as_sf(kcTracts_filtered)
kcTracts_filtered <- st_set_crs(kcTracts_filtered, st_crs(seattle.test))

# Perform the spatial join
seattle_residuals <- st_join(seattle.test, kcTracts_filtered)

# Create the color palette for the gradient
color_palette <- colorRampPalette(colors = c("#d7191c", "#fdae61", "#ffffbf", "#abd9e9", "#2c7bb6"))

# Generate a sequence of colors from the palette
palette <- color_palette(100)  # This will create a smooth gradient with 100 colors

# Plot the kcTracts_filtered as the base layer in grey
ggplot() +
  geom_sf(data = kcTracts_filtered, fill = "grey89") +  # Base layer
  geom_sf(data = seattle_residuals, aes(fill = AvgResidual), size = 0.5) +  # Residuals layer
  scale_fill_gradientn(colors = palette) +  # Gradient scale for residuals
  labs(title = "Average Residuals by Census Tracts", fill = "Avg Residual") +
  theme_void()

```

# Conclusion 

From this analysis, one can infer that housing prices in Seattle are influenced by a combination of property characteristics, demographic factors, and proximity to amenities, and there is variability in how well the model's predictions align with actual sale prices across different areas. This suggests that while the model captures broad trends, local factors and potential data issues may cause variations in prediction accuracy, which would be important for stakeholders to consider.

- The regression models suggest that variables like square footage and demographic factors have significant relationships with housing prices, indicating that larger, newer homes in areas with higher median incomes tend to fetch higher prices.
- The map showing properties by sale price reveals a clear spatial pattern in property values, with some areas consistently showcasing higher-valued properties, potentially reflecting neighborhood desirability or other location-specific advantages.
- The presence of basements seems to be a common feature in certain areas, which may correspond to the architectural style or age of the housing stock in those neighborhoods.
- Proximity to schools appears to be a factor in housing prices, as seen in the quintile distribution around educational institutions, suggesting that homes near schools may be in higher demand, affecting their market value.
- Demographic variables, like median income, shown through mapping, reflect economic disparities across different areas, which likely influence housing affordability and investment patterns.
- The attempt to visualize average residuals by census tract aimed to assess prediction errors geographically. However, the visualization challenges prevented a clear understanding of spatial patterns in model accuracy.
